Heavily separable functors of the second kind and applications

TL;DR

This paper introduces the concept of heavily separable functors of the second kind and explores their properties and applications across module categories, Eilenberg-Moore categories, and entwined modules.

Contribution

It defines heavily separable functors of the second kind and analyzes their behavior in various categorical contexts, providing new theoretical insights.

Findings

Characterization of heavy separability conditions for functors in different settings

Conditions for heavy separability in modules over small preadditive categories

Criteria for heavy separability of functors in entwined modules

Abstract

We introduce heavily separable functors of the second kind and study them in three different situations. The first of these is with restrictions and extensions of scalars for modules over small preadditive categories. The second is with free functors taking values in Eilenberg-Moore categories associated to a monad or a comonad. Finally, we consider entwined modules and give if and only if conditions for heavy separability of the second kind for functors forgetting either the comodule action or the module action.