Difference between r1.30 and the current
@@ -4,32 +4,57 @@
category에서 [[사상,morphism]]의 조건?
* 사상은 [[합성,composition]]이 가능해야 함 (morphisms must be composable)
* 사상은 자기 자신으로 가는 [[항등사상,identity_morphism]]이 존재해야 함
* ...tbw
* 사상은 자기 자신으로 가는 [[항등사상,identity_morphism]]이 존재해야 함 // (curr at [[아이덴티티,identity]])
* associativity
Informal definition[* The Language of Categories | Category Theory and Why We Care 1.1 https://youtu.be/5Ykrfqrxc8o?si=cYlD5dDwmODCbMmm&t=58]
* [[대상,object]]과 $(A,B,C,\ldots)$
* arrow([[화살,arrow]] or [[화살표,arrow]]) $(f,g,\ldots)$
가 있는데, 다음 법칙들을 만족.
* composition - [[합성,composition]]
* associativity - (maybe [[결합성,associativity]]? curr. [[VG:결합법칙,associativity]])
* identity - (curr at [[아이덴티티,identity]])
----
MKL
Pagename TBD
F대수,F-algebra ?? <- pagename: ,의 왼쪽에는 _를 고유명사(? 인명?) 좌우 외에는 안 쓰기로 했는데, -도 쓰지 말까?
[[F대수,F-algebra]] =F대수,F-algebra =,F-algebra F대수 F-algebra
{
아님 대수 대신 대수학 ?https://en.wikipedia.org/wiki/F-algebra
https://ja.wikipedia.org/wiki/F代数
} // F-algebra ... NN:F-algebra Ggl:F-algebra
의 [[쌍대,dual]]인 // [[쌍대성,duality]]
F-coalgebra
F-쌍대대수 ??
KMS는 KmsE:coalgebra = 쌍대대수 이긴 한데.
https://en.wikipedia.org/wiki/F-coalgebra
https://ja.wikipedia.org/wiki/F余代数
// F-coalgebra ... NN:F-coalgebra Ggl:F-coalgebra
QQQ F의 정확한 의미... sigma-algebra의 sigma 비슷해 보이는데
암튼 rel [[코,co]] or [[쌍대,dual]] or [[쌍대성,duality]]
{
rel
https://en.wikipedia.org/wiki/Coinduction
[[coinduction]] =,coinduction . coinduction
{
'''coinduction'''
쌍대귀납 ?
MKL [[귀납,induction]]
https://en.wikipedia.org/wiki/Coinduction
KmsE:coinduction 없음. (2023-11) [[귀납,induction]] ... 에 대한 [[쌍대귀납,coinduction]]???}
} // coinduction ... NN:coinduction Ggl:coinduction // 쌍대귀납 ... NN:쌍대귀납 Ggl:쌍대귀납
}
coalgebra 말고도 dialgebra 라는 게
이건 algebra + coalgebra 모두를 일반화 한. "In abstract algebra, a dialgebra is the generalization of both algebra and coalgebra."
@@ -43,62 +68,64 @@
{
WtEn:category_theory
https://www.euclideanspace.com/maths/discrete/category/index.htm
[[대상,object]]
[[모노이드,monoid]]
[[모노이드,monoid]]
[[대상,object]]
https://ko.wikipedia.org/wiki/모노이드_대상
https://ja.wikipedia.org/wiki/モノイド対象
}
[[모나드,monad]] ? =모나드, =,monad .
KmsE:monad
[[WtEn:monad]]
= https://en.wiktionary.org/wiki/monad
(4.) "A monoid object in the category of endofunctors of a fixed category."
[[WpEn:Monad]] = https://en.wikipedia.org/wiki/Monad
esp
[[WpEn:Monad_(category_theory)]] = https://en.wikipedia.org/wiki/Monad_(category_theory)
[[WpKo:모나드_(범주론)]] = https://ko.wikipedia.org/wiki/모나드_(범주론)
[[WpJa:モナド_(圏論)]] = https://ja.wikipedia.org/wiki/モナド_(圏論)
Cmp [[모노이드,monoid]]
{
[[WtEn:comonad]] = https://en.wiktionary.org/wiki/comonad
"A monad of the opposite category."
KmsE:comonad ?
Ggl:comonad
[[범주,category]]의 [[동치,equivalence]]: [[category_equivalence]] - w
tmp bmks ko
GitHub - pilgwon/CategoryTheory: ![번역] 프로그래머를 위한 카테고리 이론 (Category Theory for Programmers)
https://github.com/pilgwon/CategoryTheory
[[map]] / [[mapping]] ... [[사상,map]](vg)
[[functor]] =,functor . [[펑터,functor]] or [[함자,functor]] ....
{
WtEn:functor
함자
펑터
Cmp [[함수,function]]
Cmp [[pseudofunctor]] =,pseudofunctor =,pseudofunctor . pseudofunctor { pseudofunctor Ggl:pseudofunctor pseudofunctor }
----
[[morphism]] =,morphism =,morphism . 사상 morphism ... [[모피즘,morphism]]? [[사상,morphism]]?
WtEn:category_theory
Sites
Maths - Category Theory - Martin Bakerhttps://www.euclideanspace.com/maths/discrete/category/index.htm
Videos
Tutorial on Category Theory: Part 1 – Pure and Classical - YouTube
https://www.youtube.com/watch?v=6eWn9nG5d7o
Topics
[[함수,function]][[대상,object]]
[[모노이드,monoid]]
[[모노이드대상,monoid_object]] =모노이드대상,monoid_object 모노이드대상,monoid_object 모노이드대상,monoid_object
[[모노이드대상,monoid_object]]
[[모나드,monad]] ? =모나드, =,monad . monad
{https://www.euclideanspace.com/maths/discrete/category/higher/monad/index.htm
= https://en.wiktionary.org/wiki/monad
(4.) "A monoid object in the category of endofunctors of a fixed category."
esp
[[WpEn:Monad_(category_theory)]] = https://en.wikipedia.org/wiki/Monad_(category_theory)
[[WpJa:モナド_(圏論)]] = https://ja.wikipedia.org/wiki/モナド_(圏論)
Cmp [[모노이드,monoid]]
}
} // monad Ggl:"monad category theory" Ggl:"범주론 monad"
[[comonad]] =,comonad =,comonad . comonad{
[[WtEn:comonad]] = https://en.wiktionary.org/wiki/comonad
"A monad of the opposite category."
KmsE:comonad ?
Ggl:comonad
}
} // comonad Ggl:"comonad category theory" Ggl:"범주론 comonad"
[[범주,category]]의 [[동치,equivalence]]: [[category_equivalence]] - w
[[map]] / [[mapping]] ... [[사상,map]](vg)
[[functor]] =,functor . [[펑터,functor]] or [[함자,functor]] ....
{
'''functor'''
KmsE:functorWtEn:functor
함자
펑터
Cmp [[함수,function]]
Cmp [[pseudofunctor]] =,pseudofunctor =,pseudofunctor . pseudofunctor { pseudofunctor Ggl:pseudofunctor pseudofunctor }
Bing:펑터
Ggl:펑터
}
Bing:펑터 Ggl:펑터
} functor Ggl:"functor"
----
[[morphism]] =,morphism =,morphism . 사상 morphism ... [[모피즘,morphism]]? [[사상,morphism]]?
@@ -136,6 +163,7 @@
Ggl:monomorphism
Bing:"definition of monomorphism"
} // monomorphism (단형성 말고)
[[bimorphism]] =,bimorphism =,bimorphism . bimorphism
{
KmsE:bimorphism = https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=bimorphism x [[Date(2023-11-14T09:16:39)]]
Bing:"definition of monomorphism"
} // monomorphism (단형성 말고)
{
KmsE:bimorphism = https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=bimorphism x [[Date(2023-11-14T09:16:39)]]
@@ -144,6 +172,8 @@
Ndict:bimorphism ?
Ggl:bimorphism
} // bimorphism
ADDMORPHISMHERE
ADDMORPHISMHERE
Ggl:bimorphism
} // bimorphism
(그럼 mono-bi 다음 multimorphism ? Ggl:multimorphism )
ADDMORPHISMHERE
ADDMORPHISMHERE
@@ -156,6 +186,7 @@
RANDOMLINKS TOCLEANUP
[[WtEn:classifying_morphism]]
= https://en.wiktionary.org/wiki/classifying_morphism
...
Ndict:morphism
[[WtEn:classifying_morphism]]
= https://en.wiktionary.org/wiki/classifying_morphism
... [[분류,classification]]?
...
Ndict:morphism
@@ -167,16 +198,22 @@
//and [[연산자,operator]](=[[작용소,operator]]) esp [[이항연산자,binary_operator]](=[[이항작용소,binary_operator]]) 와 mkl
[[결합법칙,associativity]] (vg) =,associativity =결합 .... [[결합성,associativity]] [[결합법칙,commutative_law]] ? or rule?
{
KmsE:associativ
WtEn:associativity
https://ko.wikipedia.org/wiki/결합법칙
https://en.wikipedia.org/wiki/Associative_property
[[교환법칙,commutativity]] (vg) =,commutativity =교환 .... [[교환성,commutativity]] [[교환법칙,commutative_law]] or rule?
{
KmsE:commutativ
WtEn:commutativity
mkl
[[결합법칙,associativity]] (vg) =,associativity =결합 .... [[결합성,associativity]] [[결합법칙,commutative_law]] ? or rule?
{
'''associativity'''
'''결합성?'''
WtEn:associativity
https://ko.wikipedia.org/wiki/결합법칙
https://en.wikipedia.org/wiki/Associative_property
}
} // associativity
[[교환법칙,commutativity]] (vg) =,commutativity =교환 .... [[교환성,commutativity]] [[교환법칙,commutative_law]] or rule?
{
'''commutativity'''
'''교환성'''? 가환성?
WtEn:commutativity
mkl
@@ -187,9 +224,17 @@
[[commmutative_diagram]] - isa [[다이어그램,diagram]] or [[그림,diagram]]
https://en.wikipedia.org/wiki/Commutative_property
= bmks ko =
Bartosz Milewski's "Category Theory for Programmers" Korean translation
프로그래머를 위한 범주론
"본 레파지토리는 Bartosz Milewsk의 Category Theory for Programmers을 번역하며 학습한 레파지토리입니다."
https://en.wikipedia.org/wiki/Commutative_property
}
} // commutativity ... NN:commutativity Ggl:commutativity
----
<<tableofcontents>>
= bmks ko =
tmp bmks ko
GitHub - pilgwon/CategoryTheory: ![번역] 프로그래머를 위한 카테고리 이론 (Category Theory for Programmers)
https://github.com/pilgwon/CategoryTheory
프로그래머를 위한 범주론
"본 레파지토리는 Bartosz Milewsk의 Category Theory for Programmers을 번역하며 학습한 레파지토리입니다."
@@ -197,6 +242,10 @@
https://theworldaswillandidea.tistory.com/category/Series/함수적인%2C%20너무나%20함수적인
= bmks en =
Category theory: online lecture notes, etc. - Logic Matters
https://www.logicmatters.net/categories/
= books? =
Naver:범주론+교재
@@ -216,7 +265,15 @@
Bing:카테고리이론+서적
Bing:category+theory+book+recommendation
YouTube:카테고리이론
Bing:category+theory+book+recommendation
= watch yt =
= tmp videos en / category theory =
Category Theory in Life - Eugenia Cheng
https://youtu.be/ho7oagHeqNc?si=YQUeKoKJJzgLQp-H
The Language of Categories | Category Theory and Why We Care 1.1 - YouTube
https://www.youtube.com/watch?v=5Ykrfqrxc8o
...
YouTube:범주론YouTube:카테고리이론
@@ -228,17 +285,18 @@
= http://wiki.c2.com/?CategoryTheory
https://wiki.haskell.org/Category_theory
Sub:
[[opposite_category]] = [[dual_category]] ? // =,opposite_category opposite_category / =,dual_category dual_category
{
WtEn:dual_category ?
https://artofproblemsolving.com/wiki/index.php/Opposite_category
[[WpEn:Opposite_category]]
https://wiki.haskell.org/Category_theory
}
} // category theory
수학적 구조(mathematical_structure), [[수학,math]] [[구조,structure]]
[[mathematical_structure]] - 수학적 구조(mathematical_structure), [[수학,math]] curr at [[구조,structure?action=highlight&value=mathematical_structure]]
Sub:
[[opposite_category]] = [[dual_category]] ? // =,opposite_category opposite_category / =,dual_category dual_category
{
'''opposite category'''
(tmp) kms opposite => https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=oppositeWtEn:dual_category ?
WtEn:opposite_category ??
WtEn:opposite_category x [[Date(2024-01-12T13:57:33)]]
https://artofproblemsolving.com/wiki/index.php/Opposite_category
[[WpEn:Opposite_category]]
@@ -248,71 +306,81 @@
https://encyclopediaofmath.org/wiki/Dual_category
}
} // opposite category Ggl:"opposite category"
{
WtEn:small_category ? qqqqqqqqqqq
'''small category'''
[[WtEn:small_category]] = https://en.wiktionary.org/wiki/small_category
https://encyclopediaofmath.org/wiki/Small_category}
} // small category Ggl:"small category"
{
closed category
WtEn:closed_category ? ffffffff
'''closed category'''
WtEn:closed_category ? x [[Date(2024-01-12T13:57:33)]]
https://ko.wikipedia.org/wiki/데카르트_닫힌_범주 "Cartesian closed category, 약자 CCC"
Ggl:"closed category" Ggl:"닫힌 범주"
Naver:"closed category" Naver:"닫힌 범주"
} // closed category Ggl:"closed category" Ggl:"닫힌 범주" Naver:"closed category" Naver:"닫힌 범주"
[[bicategory]] =,bicategory =,bicategory . bicategory{
https://ko.wikipedia.org/wiki/이차_범주
https://en.wikipedia.org/wiki/Bicategory
https://encyclopediaofmath.org/wiki/Bicategory
https://ncatlab.org/nlab/show/bicategory
... Google:bicategory
[[quotient_category]] { MKLINK [[quotient_object]] [[몫,quotient]] https://encyclopediaofmath.org/wiki/Quotient_category }
} // bicategory ... Google:bicategory
[[quotient_category]]
{
'''quotient category'''
MKLINK [[quotient_object]] [[몫,quotient]] https://encyclopediaofmath.org/wiki/Quotient_category
} // quotient category Ggl:"quotient category"
[[topologized_category]] => https://encyclopediaofmath.org/wiki/Site[[Abelian_category]] { https://mathworld.wolfram.com/AbelianCategory.html https://encyclopediaofmath.org/wiki/Abelian_category }
[[Grothendieck_category]] { https://encyclopediaofmath.org/wiki/Grothendieck_category }
[[derived_category]] =,derived_category . derived_category
{ https://encyclopediaofmath.org/wiki/Derived_category }
[[derived_category]] =,derived_category . derived_category { '''derived category''' https://encyclopediaofmath.org/wiki/Derived_category } // derived category Ggl:"derived category"
[[additive_category]] =,additive_category . additive_category{
'''additive category'''
[[MathWorld:AdditiveCategory]] = https://mathworld.wolfram.com/AdditiveCategory.htmlhttps://encyclopediaofmath.org/wiki/Additive_category
}
} // additive category Ggl:"additive category"
[[subcategory]] =,subcategory . subcategory - w{
subcategory
'''subcategory'''
부범주? 부분범주?https://mathworld.wolfram.com/Subcategory.html
[[WtEn:subcategory]] = https://en.wiktionary.org/wiki/subcategory
https://ncatlab.org/nlab/show/subcategory
}
} // subcategory Ggl:subcategory
[[supercategory]] =,supercategory . supercategory - w{
'''supercategory'''
[[WtEn:supercategory]] = https://en.wiktionary.org/wiki/supercategory}
} // supercategory Ggl:supercategory
[[metacategory]] =,metacategory =,metacategory . metacategory
{
'''metacategory'''
메타범주?WtEn:metacategory
Ndict:metacategory
MKLINK [[metagraph]] =,metagraph =,metagraph . metagraph { https://proofwiki.org/wiki/Definition:Metagraph }
MKLINK [[metagraph]] =,metagraph =,metagraph . metagraph { https://proofwiki.org/wiki/Definition:Metagraph } [[메타,meta]]
https://proofwiki.org/wiki/Definition:Metacategory}
distributive_lattice { https://ncatlab.org/nlab/show/distributive+lattice
KmsE:"distributive lattice": 분배격자
...
Naver:distributive+lattice
Ggl:distributive+lattice
} // metacategory Ggl:metacategory
[[distributive_lattice]] =,distributive_lattice . distributive_lattice
{
'''distributive lattice'''
WtEn:distributive_lattice
https://ncatlab.org/nlab/show/distributive+lattice
KmsE:"distributive lattice": 분배격자
} // distributive lattice ... Naver:distributive+lattice Ggl:distributive+lattice
= MKLINK =[[대상,object]]
category에서 사상,morphism의 조건?
- 사상은 합성,composition이 가능해야 함 (morphisms must be composable)
- 사상은 자기 자신으로 가는 항등사상,identity_morphism이 존재해야 함 // (curr at 아이덴티티,identity)
- associativity
Informal definition[1]
가 있는데, 다음 법칙들을 만족.
가 있는데, 다음 법칙들을 만족.
- composition - 합성,composition
- associativity - (maybe 결합성,associativity? curr.
결합법칙,associativity)
- identity - (curr at 아이덴티티,identity)
MKL
Pagename TBD
F-대수,F-algebra ??
F대수,F-algebra ?? <- pagename: ,의 왼쪽에는 _를 고유명사(? 인명?) 좌우 외에는 안 쓰기로 했는데, -도 쓰지 말까?
F대수,F-algebra =F대수,F-algebra =,F-algebra F대수 F-algebra
{
아님 대수 대신 대수학 ?
https://en.wikipedia.org/wiki/F-algebra
https://ja.wikipedia.org/wiki/F代数
} // F-algebra ...
F-algebra
F-algebra
F대수,F-algebra ?? <- pagename: ,의 왼쪽에는 _를 고유명사(? 인명?) 좌우 외에는 안 쓰기로 했는데, -도 쓰지 말까?
F대수,F-algebra =F대수,F-algebra =,F-algebra F대수 F-algebra
{
아님 대수 대신 대수학 ?
https://en.wikipedia.org/wiki/F-algebra
https://ja.wikipedia.org/wiki/F代数
} // F-algebra ...
![NN: NN:](/wiki/imgs/interwiki/nn-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
F-coalgebra
F-쌍대대수 ??
KMS는
coalgebra = 쌍대대수 이긴 한데.
https://en.wikipedia.org/wiki/F-coalgebra
https://ja.wikipedia.org/wiki/F余代数
// F-coalgebra ...
F-coalgebra
F-coalgebra
F-쌍대대수 ??
KMS는
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
https://en.wikipedia.org/wiki/F-coalgebra
https://ja.wikipedia.org/wiki/F余代数
// F-coalgebra ...
![NN: NN:](/wiki/imgs/interwiki/nn-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
QQQ F의 정확한 의미... sigma-algebra의 sigma 비슷해 보이는데
암튼 rel 코,co or 쌍대,dual or 쌍대성,duality
{
rel
coinduction =,coinduction . coinduction
{
rel
coinduction =,coinduction . coinduction
{
coinduction
쌍대귀납 ?
MKL 귀납,induction
https://en.wikipedia.org/wiki/Coinduction
coinduction없음. (2023-11) 귀납,induction ... 에 대한 쌍대귀납,coinduction???
} // coinduction ...
coinduction
coinduction // 쌍대귀납 ...
쌍대귀납
쌍대귀납
} coinduction
쌍대귀납 ?
MKL 귀납,induction
https://en.wikipedia.org/wiki/Coinduction
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
} // coinduction ...
![NN: NN:](/wiki/imgs/interwiki/nn-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![NN: NN:](/wiki/imgs/interwiki/nn-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
coalgebra 말고도 dialgebra 라는 게
이건 algebra + coalgebra 모두를 일반화 한. "In abstract algebra, a dialgebra is the generalization of both algebra and coalgebra."
https://en.wikipedia.org/wiki/Dialgebra
https://ncatlab.org/nlab/show/dialgebra
이건 algebra + coalgebra 모두를 일반화 한. "In abstract algebra, a dialgebra is the generalization of both algebra and coalgebra."
https://en.wikipedia.org/wiki/Dialgebra
https://ncatlab.org/nlab/show/dialgebra
Sites
Maths - Category Theory - Martin Baker
https://www.euclideanspace.com/maths/discrete/category/index.htm
Maths - Category Theory - Martin Baker
https://www.euclideanspace.com/maths/discrete/category/index.htm
Videos
Tutorial on Category Theory: Part 1 – Pure and Classical - YouTube
https://www.youtube.com/watch?v=6eWn9nG5d7o
Tutorial on Category Theory: Part 1 – Pure and Classical - YouTube
https://www.youtube.com/watch?v=6eWn9nG5d7o
Topics
함수,function
대상,object
모노이드,monoid
모노이드대상,monoid_object
모나드,monad ? =모나드, =,monad . monad
{
monad
함수,function
대상,object
모노이드,monoid
모노이드대상,monoid_object
모나드,monad ? =모나드, =,monad . monad
{
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
= https://en.wiktionary.org/wiki/monad
(4.) "A monoid object in the category of endofunctors of a fixed category."
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
esp
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
![WpKo: WpKo:](/wiki/imgs/interwiki/wpko-16.png)
![WpJa: WpJa:](/wiki/imgs/interwiki/wpja-16.png)
Cmp 모노이드,monoid
} // monad
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
comonad =,comonad =,comonad . comonad
{
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
"A monad of the opposite category."
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
} // comonad
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
functor =,functor . 펑터,functor or 함자,functor ....
{
functor
functor
functor
함자
펑터
Cmp 함수,function
Cmp pseudofunctor =,pseudofunctor =,pseudofunctor . pseudofunctor { pseudofunctor
pseudofunctor pseudofunctor }
펑터
펑터
} functor
functor
{
functor
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
함자
펑터
Cmp 함수,function
Cmp pseudofunctor =,pseudofunctor =,pseudofunctor . pseudofunctor { pseudofunctor
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
} functor
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
morphism =,morphism =,morphism . 사상 morphism ... 모피즘,morphism? 사상,morphism?
{
morphism
morphism =
{
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
- 형태(셰이프,shape 피겨,figure ....)에 대한 것. 이건 몇 개 안 됨.
- 수학의 일반적인 뜻(esp 범주, 함수, 사상) - 보통 사상,morphism으로 번역되는 - 사상,map 사상,mapping 함수,function 연산,operation 연산자,operator 변환,transformation(curr 변환)과 거의 같은 그거
- ex. (수없이 많이 추가될것이므로 아래에)
- ex. (수없이 많이 추가될것이므로 아래에)
사상
모피즘 ? // transliteration: morphism-모피즘 맞는듯, via '이소모피즘-isomorphism' via kornorms. / 근데 저 예 하나는 아이소에 가깝지 않나. 영어로는? -
isomorphism : "/àisəmɔ́:rfizm/". Yes, 아이소에 가까움.
모피즘 ? // transliteration: morphism-모피즘 맞는듯, via '이소모피즘-isomorphism' via kornorms. / 근데 저 예 하나는 아이소에 가깝지 않나. 영어로는? -
![NdEn: NdEn:](/wiki/imgs/interwiki/nden-16.png)
MKL
동형사상,isomorphism
자기동형사상,automorphism
자기사상,endomorphism
준동형사상,homomorphism //
homomorphism = https://en.wiktionary.org/wiki/homomorphism
monomorphism =,monomorphism =,monomorphism . monomorphism // 단형성,monomorphism 말고
multimorphism )
ADDMORPHISMHERE
ADDMORPHISMHERE
ADDMORPHISMHERE
ADD_MORPHISM_HERE
ADD_MORPHISM_HERE
ADD_MORPHISM_HERE
동형사상,isomorphism
자기동형사상,automorphism
자기사상,endomorphism
준동형사상,homomorphism //
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
monomorphism =,monomorphism =,monomorphism . monomorphism // 단형성,monomorphism 말고
{
monomorphism
monomorphism = https://en.wiktionary.org/wiki/monomorphism
Monomorphism = 666666666666666666666777777777777 ??
...
monomorphism
monomorphism
definition of monomorphism
} // monomorphism (단형성 말고)
bimorphism =,bimorphism =,bimorphism . bimorphismmonomorphism
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
- 수학에선 " an injective homomorphism"
- 생물학에선 sexual_dimorphism (sexual
dimorphism )의 absense. 저건뭐냐?
sexual dimorphism = https://terms.naver.com/search.naver?query=sexual dimorphism
즉 암수의 뚜렷한 형태 차이점? chk
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
...
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
} // monomorphism (단형성 말고)
{
bimorphism = https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=bimorphism x 2023-11-14
bimorphism = https://en.wiktionary.org/wiki/bimorphism
bimorphism ?
bimorphism
} // bimorphism
(그럼 mono-bi 다음 multimorphism ? ![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
"A morphism which is both a monomorphism and an epimorphism."
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
} // bimorphism
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
ADDMORPHISMHERE
ADDMORPHISMHERE
ADD_MORPHISM_HERE
ADD_MORPHISM_HERE
ADD_MORPHISM_HERE
RANDOMLINKS TOCLEANUP
classifying_morphism
= https://en.wiktionary.org/wiki/classifying_morphism
...
morphism
morphism
} // morphism
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
= https://en.wiktionary.org/wiki/classifying_morphism
...
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
} // morphism
//이하 연산,operation esp 이항연산,binary_operator
//and 연산자,operator(=작용소,operator) esp 이항연산자,binary_operator(=이항작용소,binary_operator) 와 mkl
결합법칙,associativity (vg) =,associativity =결합 .... 결합성,associativity 결합법칙,commutative_law ? or rule?
{
associativity
결합성?
//and 연산자,operator(=작용소,operator) esp 이항연산자,binary_operator(=이항작용소,binary_operator) 와 mkl
결합법칙,associativity (vg) =,associativity =결합 .... 결합성,associativity 결합법칙,commutative_law ? or rule?
{
associativity
결합성?
https://ko.wikipedia.org/wiki/결합법칙
https://en.wikipedia.org/wiki/Associative_property
} // associativity
https://en.wikipedia.org/wiki/Associative_property
} // associativity
교환법칙,commutativity (vg) =,commutativity =교환 .... 교환성,commutativity 교환법칙,commutative_law or rule?
{
commutativity
교환성? 가환성?
{
commutativity
교환성? 가환성?
https://en.wikipedia.org/wiki/Commutative_property
} // commutativity ...
commutativity
commutativity
} // commutativity ...
![NN: NN:](/wiki/imgs/interwiki/nn-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
1. bmks ko ¶
tmp bmks ko
GitHub - pilgwon/CategoryTheory: [번역] 프로그래머를 위한 카테고리 이론 (Category Theory for Programmers)
https://github.com/pilgwon/CategoryTheory
GitHub - pilgwon/CategoryTheory: [번역] 프로그래머를 위한 카테고리 이론 (Category Theory for Programmers)
https://github.com/pilgwon/CategoryTheory
Bartosz Milewski's "Category Theory for Programmers" Korean translation
프로그래머를 위한 범주론
"본 레파지토리는 Bartosz Milewsk의 Category Theory for Programmers을 번역하며 학습한 레파지토리입니다."
https://github.com/alstn2468/category-theory-for-programmers
프로그래머를 위한 범주론
"본 레파지토리는 Bartosz Milewsk의 Category Theory for Programmers을 번역하며 학습한 레파지토리입니다."
https://github.com/alstn2468/category-theory-for-programmers
2. bmks en ¶
Category theory: online lecture notes, etc. - Logic Matters
https://www.logicmatters.net/categories/
https://www.logicmatters.net/categories/
4. tmp videos en / category theory ¶
The Language of Categories | Category Theory and Why We Care 1.1 - YouTube
https://www.youtube.com/watch?v=5Ykrfqrxc8o
https://www.youtube.com/watch?v=5Ykrfqrxc8o
mathematical_structure - 수학적 구조(mathematical_structure), 수학,math curr at 구조,structure?action=highlight&value=mathematical_structure
Sub:
opposite_category = dual_category ? // =,opposite_category opposite_category / =,dual_category dual_category
{
opposite category
(tmp) kms opposite => https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=opposite
opposite_category = dual_category ? // =,opposite_category opposite_category / =,dual_category dual_category
{
opposite category
(tmp) kms opposite => https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=opposite
https://artofproblemsolving.com/wiki/index.php/Opposite_category
Opposite_category
...
opposite_category
opposite_category
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
...
![Google: Google:](/wiki/imgs/interwiki/google-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
small_category =,small_category . small_category
{
small category
small_category = https://en.wiktionary.org/wiki/small_category
https://encyclopediaofmath.org/wiki/Small_category
} // small category
small category
{
small category
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://encyclopediaofmath.org/wiki/Small_category
} // small category
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
closed_category =,closed_category . closed_category
{
closed category
closed_category ? x 2024-01-12
{
closed category
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://encyclopediaofmath.org/wiki/Closed_category
https://ko.wikipedia.org/wiki/데카르트_닫힌_범주 "Cartesian closed category, 약자 CCC"
https://ko.wikipedia.org/wiki/데카르트_닫힌_범주 "Cartesian closed category, 약자 CCC"
bicategory =,bicategory =,bicategory . bicategory
{
https://ko.wikipedia.org/wiki/이차_범주
https://en.wikipedia.org/wiki/Bicategory
https://encyclopediaofmath.org/wiki/Bicategory
https://ncatlab.org/nlab/show/bicategory
} // bicategory ...
bicategory
{
https://ko.wikipedia.org/wiki/이차_범주
https://en.wikipedia.org/wiki/Bicategory
https://encyclopediaofmath.org/wiki/Bicategory
https://ncatlab.org/nlab/show/bicategory
} // bicategory ...
![Google: Google:](/wiki/imgs/interwiki/google-16.png)
quotient_category
Abelian_category { https://mathworld.wolfram.com/AbelianCategory.html https://encyclopediaofmath.org/wiki/Abelian_category }
Grothendieck_category { https://encyclopediaofmath.org/wiki/Grothendieck_category }
derived_category =,derived_category . derived_category { derived category https://encyclopediaofmath.org/wiki/Derived_category } // derived category
derived category
additive_category =,additive_category . additive_category
{
additive category
AdditiveCategory = https://mathworld.wolfram.com/AdditiveCategory.html
https://encyclopediaofmath.org/wiki/Additive_category
} // additive category
additive category
subcategory =,subcategory . subcategory - w
{
subcategory
부범주? 부분범주?
https://mathworld.wolfram.com/Subcategory.html
subcategory = https://en.wiktionary.org/wiki/subcategory
https://ncatlab.org/nlab/show/subcategory
} // subcategory
subcategory
supercategory =,supercategory . supercategory - w
{
supercategory
supercategory = https://en.wiktionary.org/wiki/supercategory
} // supercategory
supercategory
{
quotient category
MKLINK quotient_object 몫,quotient https://encyclopediaofmath.org/wiki/Quotient_category
} // quotient category
quotient category
topologized_category => https://encyclopediaofmath.org/wiki/Sitequotient category
MKLINK quotient_object 몫,quotient https://encyclopediaofmath.org/wiki/Quotient_category
} // quotient category
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
Abelian_category { https://mathworld.wolfram.com/AbelianCategory.html https://encyclopediaofmath.org/wiki/Abelian_category }
Grothendieck_category { https://encyclopediaofmath.org/wiki/Grothendieck_category }
derived_category =,derived_category . derived_category { derived category https://encyclopediaofmath.org/wiki/Derived_category } // derived category
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
additive_category =,additive_category . additive_category
{
additive category
![MathWorld: MathWorld:](/wiki/imgs/interwiki/mathworld-16.png)
https://encyclopediaofmath.org/wiki/Additive_category
} // additive category
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
subcategory =,subcategory . subcategory - w
{
subcategory
부범주? 부분범주?
https://mathworld.wolfram.com/Subcategory.html
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://ncatlab.org/nlab/show/subcategory
} // subcategory
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
supercategory =,supercategory . supercategory - w
{
supercategory
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
} // supercategory
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
MKLINK metagraph =,metagraph =,metagraph . metagraph { https://proofwiki.org/wiki/Definition:Metagraph } 메타,meta
https://proofwiki.org/wiki/Definition:Metacategory
} // metacategory
metacategory
distributive_lattice =,distributive_lattice . distributive_lattice
https://proofwiki.org/wiki/Definition:Metacategory
} // metacategory
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
distributive_lattice =,distributive_lattice . distributive_lattice
{
distributive lattice
distributive_lattice
https://ncatlab.org/nlab/show/distributive lattice
distributive lattice: 분배격자
} // distributive lattice ...
distributive lattice
distributive lattice
distributive lattice
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://ncatlab.org/nlab/show/distributive lattice
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
} // distributive lattice ...
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
6.1. categorification ¶
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
= https://en.wiktionary.org/wiki/categorification
"A procedure that defines theorems정리,theorem in terms of category theory by mapping concepts from set theory집합론,set_theory to category theory범주론,category_theory."
6.2. decategorification ¶
decategorification
decategorification =,decategorification =,decategorification . decategorification
{
decategorification =,decategorification =,decategorification . decategorification
{
https://ncatlab.org/nlab/show/decategorification
decategorification
decategorification
decategorification
}
"process which turns a category into a set "
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
decategorification
}
7. 이상엽 ¶
// from https://www.youtube.com/watch?v=aggoIxEkr6Q 범주론 category theory 이란?
(0:29)
범주란?
범주의 두 요소
- 대상의 모임
- 사상의 모임
- 대상,object의 모임 ob(C)
- 임의의 두 대상 X,Y∈ob(C)에 대해 X를 정의역,domain, Y를 공역,codomain으로 하는 사상,map f:X→Y의 모임 hom(X,Y)
(6:50)
집합론적 함수와의 비교 // 집합론,set_theory
1≤2에서 ≤는 집합론에서 말하는 함수는 아니다. 근데 범주론에선 사상이다.
- 집합론이 집합,set을 주 대상으로 하고 이로부터 함수가 파생되는 구조를 가지고 있다면,
범주론은 함수가 주 대상이고 이로부터 파생된 대상의 성질을 연구한다.
- 범주의 대상은 집합일 필요가 없으며, 사상,morphism도 함수,function일 필요가 없다.
ex. 자연수,natural_number(대상,object)에 대해 부등호 ≤는 사상일 수 있다. 즉 1≤2를 1→2로 볼 수 있다.
1≤2에서 ≤는 집합론에서 말하는 함수는 아니다. 근데 범주론에선 사상이다.
9. files ¶
Category Theory / Randall R. Holmes / October 8, 2019
99p
https://web.auburn.edu/holmerr/8970/Textbook/CategoryTheory.pdf
99p
https://web.auburn.edu/holmerr/8970/Textbook/CategoryTheory.pdf
Notes on Category Theory / with examples from basic mathematics / Paolo Perrone http://www.paoloperrone.org / Last update: February 2021
181p
https://arxiv.org/pdf/1912.10642.pdf
181p
https://arxiv.org/pdf/1912.10642.pdf
10. 같은영단어 ¶
카테고리,category - via kornorms.
Sub:
----
- [1] The Language of Categories | Category Theory and Why We Care 1.1 https://youtu.be/5Ykrfqrxc8o?si=cYlD5dDwmODCbMmm&t=58