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Results tagged with ct.category-theory
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user 3664
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
4
votes
2
answers
1k
views
Intuition for the satellite of a functor
Occasionally in math I come across constructions or tools that are a bit convoluted. I can look at these constructions and see that they indeed perform the task they were made to do, but sometimes I c …
- 855
6
votes
1
answer
348
views
Significance of the vanishing of $K_{-1}(A)$
In M. Schlichting's paper, he defines the negative $K$-theory for derived categories. In this he states that for $\mathcal{A}$ an idempotent complete (see below) triangulated category, $K_{-1}(\mathca …
- 855
8
votes
0
answers
120
views
Positive definite kernels on categories
I'm wondering if there is any work on studying positive definite kernels on (the objects of a) category. By this I mean for a category $\mathcal{C}$, find a function
$$
K: Ob\mathcal{C} \times Ob\mat …
- 855
9
votes
Is there a nice application of category theory to functional/complex/harmonic analysis?
At the suggestion of Yemon, I have moved my comment to an answer. The [Gelfand representation][1]
[1]: http://en.wikipedia.org/wiki/Gelfand_representation
gives an equivalence between the category of …
7
votes
4
answers
995
views
`Topos' with alternate subobject lattice?
We know that for any topos E, and for any object A in E, the subobjects of A, Sub(A), form a Heyting lattice.
Does anybody know of any sort of modification of the definition of a topos that makes Sub …
- 855
39
votes
5
answers
6k
views
Why do categorical foundationalists want to escape set theory?
This is a question that I have seen asked passively in comments relating to the separation of category theory from set theory, but I haven't seen it addressed in full.
I know that it's possible to fo …
- 855