Categorification in mathematics - 편집 역사

2020년 11월 14일 (토) 00:40에 Pythagoras0님의 편집

2020-11-14T00:40:33Z

2020년 11월 13일 (금) 10:40에 imported>Pythagoras0님의 편집

2020-11-13T10:40:00Z

imported>Pythagoras0: /* related items */

2015-09-08T07:47:07Z

2015년 6월 15일 (월) 00:54에 imported>Pythagoras0님의 편집

2015-06-15T00:54:08Z

imported>Pythagoras0: 새 문서: ==introduction== * general motivation for categorification * algebraic/geometric structures <-> category * we can use general properties of the category $\mathcal{C}$ * It's a long es...

2015-06-15T00:50:46Z

새 문서: ==introduction== * general motivation for categorification * algebraic/geometric structures <-> category * we can use general properties of the category $\mathcal{C}$ * It's a long es...

새 문서

==introduction==
* general motivation for categorification
* algebraic/geometric structures <-> category
* we can use general properties of the category $\mathcal{C}$
* It's a long established principle that an interesting way to think about numbers as the sizes of sets or dimensions of vector spaces, or better yet, the Euler characteristic of complexes.
* You can't have a map between numbers, but you can have one between sets or vector spaces.
* For example, Euler characteristic of topological spaces is not functorial, but homology is.
* One can try to extend this idea to a bigger stage, by, say, taking a vector space, and trying to make a category by defining morphisms between its vectors.
* This approach (interpreted suitably) has been a remarkable success with the representation theory of semi-simple Lie algebras (and their associated quantum groups).

← 이전 판		2020년 11월 13일 (금) 10:40 판
17번째 줄:		17번째 줄:
	==articles==		==articles==
	* Matsuoka, Takuo. “A Generalization of Categorification, and Higher ‘Theory’ of Algebras.” arXiv:1509.01582 [math], September 7, 2015. http://arxiv.org/abs/1509.01582.		* Matsuoka, Takuo. “A Generalization of Categorification, and Higher ‘Theory’ of Algebras.” arXiv:1509.01582 [math], September 7, 2015. http://arxiv.org/abs/1509.01582.
		+	[[분류:migrate]]

← 이전 판		2015년 9월 8일 (화) 07:47 판
13번째 줄:		13번째 줄:
	* [[Categorification of quantum groups]]		* [[Categorification of quantum groups]]
	* [[Monoidal categorifications of cluster algebras]]		* [[Monoidal categorifications of cluster algebras]]
		+
		+
		+	==articles==
		+	* Matsuoka, Takuo. “A Generalization of Categorification, and Higher ‘Theory’ of Algebras.” arXiv:1509.01582 [math], September 7, 2015. http://arxiv.org/abs/1509.01582.

← 이전 판		2015년 6월 15일 (월) 00:54 판
8번째 줄:		8번째 줄:
	* One can try to extend this idea to a bigger stage, by, say, taking a vector space, and trying to make a category by defining morphisms between its vectors.		* One can try to extend this idea to a bigger stage, by, say, taking a vector space, and trying to make a category by defining morphisms between its vectors.
	* This approach (interpreted suitably) has been a remarkable success with the representation theory of semi-simple Lie algebras (and their associated quantum groups).		* This approach (interpreted suitably) has been a remarkable success with the representation theory of semi-simple Lie algebras (and their associated quantum groups).
		+
		+
		+	==related items==
		+	* [[Categorification of quantum groups]]
		+	* [[Monoidal categorifications of cluster algebras]]

@@ 2번째 줄: / 2번째 줄: @@
 * general motivation for categorification
 * algebraic/geometric structures <-> category
-* we can use general properties of the category $\mathcal{C}$
+* we can use general properties of the category <math>\mathcal{C}</math>
 * It's a long established principle that an interesting way to think about numbers as the sizes of sets or dimensions of vector spaces, or better yet, the Euler characteristic of complexes.
 * You can't have a map between numbers, but you can have one between sets or vector spaces.