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Results tagged with ct.category-theory
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user 18355
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
4
votes
0
answers
561
views
Ind-objects in a coherent category
For a poset $P$, an ideal of $P$ is a downward closed upward filtered set of elements of $P$. The collection of ideals of $P$ ordered by inclusion is the free cocompletion of $P$ w.r.t. filtered colim …
- 291
5
votes
0
answers
504
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Categorifying idempotent relations
Generalizing partial orders: A relation $R$ is transitive if $R \circ R \subseteq R$ and interpolative if $R \subseteq R \circ R$. It is idempotent if $R \circ R = R$. Interpolativeness means that whe …
3
votes
1
answer
832
views
A category being self-dual vs. it being a groupoid
What is the relationship between self-duality and groupoid-ness? Does any condition imply the other? Is there an example which helps understand the difference?
To go from a self-duality $F$ on a cate …
- 291
7
votes
1
answer
446
views
Coverage, itself considered as a presheaf
A coverage $J$ on a category $C$ assigns to an object $U$ of $C$ a set of covering families $J(U)$. The covering families are required to be stable under pullback, which amounts to requiring that for …
- 291