When is the diagonal functor Frobenius?

Details When is the diagonal functor Frobenius? When is the diagonal functor Frobenius?

2009-02-23

arxiv.org/abs/0902.4012v5

Mathematics

Category Theory

18 pages; changed definition 2.1+minor modifications; submitted

Scientific paper

Given a complete, cocomplete category $\mathcal C$, we investigate the problem of describing those small categories $I$ such that the diagonal functor $\Delta:\mathcal C\to {\rm Functors}(I,\mathcal C)$ is a Frobenius functor. This condition can be rephrased by saying that the limits and the colimits of functors $I\to\mathcal C$ are naturally isomorphic. We find necessary conditions on $I$ for a certain class of categories $\mathcal C$, and, as an application, we give both necessary and sufficient conditions in the two special cases $\mathcal C={\bf Set}$ or $_R\mathcal M$, the category of left modules over a ring $R$.

Affiliated with

Also associated with

No associations

Rating

When is the diagonal functor Frobenius? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with When is the diagonal functor Frobenius?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and When is the diagonal functor Frobenius? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-171511