2023/01/23 by Positselski, Leonid
#Category Theory (math.CT) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2301.09561
In this paper we consider a conilpotent coalgebra C over a field k. Let Υ\colon C\textsf-Comod\longrightarrow C^*\textsf-Mod be the natural functor of inclusion of the category of C-comodules into the category of C^*-modules, and let Θ\colon C\textsf-Contra\longrightarrow C^*\textsf-Mod be the natural forgetful functor. We prove that the functor Υ induces a fully faithful triangulated functor on bounded (below) derived categories if and only if the functor Θ induces a fully faithful triangulated functor on bounded (above) derived categories, and if and only if the k-vector space ExtCn(k,k) is finite-dimensional for all n≥0. We call such coalgebras "weakly finitely Koszul".