Adjoint Functors

So last post I gave a (hurried) description of why adjoint pairs of functors are linked to this notion of “similar structure” between two categories.  In this post, I want to relate adjunctions to universal properties, and ultimately why we like adjoint pairs so much.     Say we’re working with the “free group on

Isomorphism, Equivalence, and Adjunction

Isomorphism As mathematicians are wont to do, whenever we have a collection of algebraic “objects,” we want to know how to “relate” them.  In the case of categories, we saw earlier that maps called functors are what we want to examine. The next step after defining these structure preserving maps is to wonder what it means