On reflective-coreflective equivalence and associated pairs

TL;DR

This paper establishes a precise condition under which reflective and coreflective subcategories exhibit a maximal-normal type equivalence, linking it to the concept of associated pairs as defined by Kelly and Lawvere.

Contribution

It characterizes when a reflective/coreflective pair satisfies a maximal-normal equivalence, connecting it to the notion of associated pairs in category theory.

Findings

Maximal-normal equivalence characterized for reflective/coreflective pairs.

Connected the equivalence condition to Kelly and Lawvere's associated pairs.

Provides a categorical criterion for associated pairs.

Abstract

We show that a reflective/coreflective pair of full subcategories satisfies a "maximal-normal"-type equivalence if and only if it is an associated pair in the sense of Kelly and Lawvere.