ON CATEGORIES OF MONOID-ACTIONS

摘要

Given a monoidal categoryBand a category S of monoids inBwe study the category MODSof all actions of monoids from S on B-objects. This is mainly done by investigation of the underlying functor V: MODS→ SxB. In particular V creates limits; filtered colimits and arbitrary colimits are detected, provided the monoidal structure behaves nicely with respect to these constructions. Moreover MODScontains B as a full coreflective subcategory; S is contained as a full reflective (and coreflective) one provided B has a terminal (zero) object. Monadicity of MODSover B is discussed as well.