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Results tagged with ct.category-theory
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user 750
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
8
votes
Accepted
Do affine schemes form a Mal'cev category?
(This is a repeat of an above comment.) The category of affine schemes is not Mal'cev. This can be disproven by producing an reflexive, non-symmetric relation on an affine scheme $X$ whose graph is …
- 13k
10
votes
1
answer
806
views
Subcategories which still give a Yoneda embedding
If $\mathbf{C}$ is a category, then the Yoneda functor which sends $a$ to $Hom_\mathbf{C}(-,a)$ is a fully faithful embedding of categories
$$ \mathbf{C}\rightarrow \mathbf{Func}(\mathbf{C}^{op},\mat …
- 13k
110
votes
11
answers
13k
views
Why do Groups and Abelian Groups feel so different?
Groups are naturally "the symmetries of an object". To me, the group axioms are just a way of codifying what the symmetries of an object can be so we can study it abstractly.
However, this heuristic …
- 13k
17
votes
3
answers
1k
views
Freyd-Mitchell for triangulated categories?
Is there a nice analog of the Freyd-Mitchell theorem for triangulated categories (potentially with some requirements)? Freyd-Mitchell is the theorem which says that any small abelian category is a fu …
- 13k
4
votes
What is an obviously coordinate-independent description of the Chevellay-Eilenberg complex f...
I believe an approach that works is to define the Chevalley-Eilenberg complex as a kind of `Koszul complex over the ring of functions'. The enveloping algebra $U$ is relatively quadratic over the rin …
- 13k