On functor-quotients and their isomorphism theorems

Abstract

The standard categorical notion of a categorical quotient is insufficient, in that it fails to recover the expected quotients in certain categories. We present an alternative formulation of F-quotients in a category C, which are relativized to a faithful functor F : C → D. The isomorphism theorems of universal algebras generalize to this setting, and we additionally find important links between F-quotients in the concrete category of first-order structures, and quotients defined for model-theoretic equivalence classes.