A characterization of the image of Comod: Coalg(R) --> Cat/(R-Mod)

Paddy McCrudden – 21 May 1997

let G: C --> R-mod be any category over R-Mod. we give necessary and sufficient conditions on G such that there exists K:C--> comod(H) some coalgebra H such that K is an equivalence and KU=G, where U is the forgetful functor U:comod(H) -->r-mod. an application includes an "explanation" of the equivalence of chaincomplexes and comodules for some coalgebra C. max kelly and steve pointed out that this proposition may be true in more general categories than r-mod.