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Results tagged with ct.category-theory
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user 136562
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
11
votes
Accepted
Has the Isbell–Freyd criterion ever been used to check that a category is concretisable?
An inverse category can be defined as a category where every $f$ admits a unique regular inverse, i.e. a map $g$ such that $fgf=f$ and $gfg=g$. In [1], Kastl proves that any locally small inverse cate …
- 631
11
votes
Accepted
Naturality up to (inner) automorphism?
Assuming the inner automorphisms you get are assumed to satisfy some further coherency conditions, your morphisms should amount to pseudonatural transformations. This requires thinking of the category …
- 631
15
votes
1
answer
406
views
Surprising invertibility results
There are results in category theory that imply that some morphism is invertible when a priori one might not have expected it. For instance,
Given a monoidal natural transformation $\tau$ between str …
2
votes
Accepted
Strict 2-Category with Lax Tensor?
This suggests that the monoidal product $\otimes\colon \mathbf{C}^2\to \mathbf{C}$ is a lax functor (see e.g. here or section 4.1 here) instead of a strict 2-functor. If so, this determines which coh …
- 631
10
votes
Accepted
Why does the 2-category of groups have (some, strict) coinserters but not (strict) inserters?
One viewpoint goes as follows: the 2-categorical structure on groups can be seen as coming from inner automorphisms, so that a 2-cell is given by an inner automorphism that translates one map to the o …
- 631