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Results tagged with ct.category-theory
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user 343
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
27
votes
What's a groupoid? What's a good example of a groupoid?
A groupoid is a generalization of a group. The easiest definition, IMO, is as a category in which all arrows are isomorphisms. So a group is just a groupoid with one object and arrows the elements of …
8
votes
9
answers
2k
views
"Surprising" categorical equivalences
This is inspired by this question about the equivalence between the category of finite sets and non-negative integers. Now this question was (rightly, I guess) closed, but the fact was surprising to t …
7
votes
References for homotopy colimit
A good (if kind of old) reference is Vogt's "Homotopy Limits and Colimits". I can't find a free reference for it, but if you can't access it, I could email a pdf (if that's allowed here).
Also, in th …
- 1,422
7
votes
3
answers
2k
views
Crossed module structure on homotopy groups
A crossed module is a pair of groups $C$ and $G$, an action of $G$ on $C$, and a homomorphism $\partial: C \to G$ that satisfy
$\partial(g\cdot c)=g(\partial c)g^{-1}$, and
$cc'c^{-1}=(\partial c) …
- 1,422
3
votes
2
answers
528
views
Classifying space of large category?
Whenever I've seen the definition of the classifying space of a category, the category is always specified to be small. I understand the definition well enough for my purposes (I think), but it occurr …
- 1,422