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Results tagged with ct.category-theory
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user 166165
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
11
votes
2
answers
1k
views
What is the category of covariant and contravariant functors?
Let $\bf Cat'$ be the category that has as objects small categories $A, B...$, and as arrows functors $F:A\to B$ that are either covariant or contravariant. The identity on $A\in\bf Cat'$ is the usual …
- 347
1
vote
1
answer
126
views
Products in discrete fibrations
Let $B$ be a category with products and let $F:A\to B$ be a discrete opfibration.
Let $F^*:B\to \bf Set$ be the functor corresponding to $F$ under the Grothendieck correspondence.
The following propos …
- 347
6
votes
0
answers
212
views
Is the category of projections interesting?
Let $C$ be a category and let $C'$ be the wide subcategory whose maps are projections, that is maps in $C$ which belong to some limiting cone (over a discrete base). Since limiting cones compose, $C'$ …
- 347
6
votes
1
answer
332
views
When is an object determined by the number of maps from the other objects?
Let $C$ be a category with finite hom-sets.
Suppose that $X$ and $Y$ are objects in $C$ such that $C(Z,X)\cong C(Z,Y)$ for any Z (with no naturality condition).
For which categories $C$ does it follow …
- 347