2009/02/23 by Chirvasitu, Alexandru
#18A30 #18A35 #18A40 #18B05 #18B40 #Category Theory (math.CT) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.0902.4012
Given a complete, cocomplete category \mathcal C, we investigate the problem of describing those small categories I such that the diagonal functor Δ:\mathcal C→ \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→\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.