Almost Split Sequences for Comodules

William Chin,  DePaul Univ.
Mark Kleiner,  Syracuse Univ.
Declan Quinn,  Syracuse Univ.

preprint

abstract:  We introduce a coalgebraic version of the transpose using the cohom functor.  Under certain finiteness conditions we show that almost split sequences exist. Our results apply to right semiperfect coalgebras such that I(S)/S is finite-dimensional for every simple right comodule S where I(S) is the injective hull of S.   For these coalgebras, there exists an almost split sequence starting at M for every finite-dimensional comodule M.