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 onContinue reading “Adjoint Functors”

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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 meansContinue reading “Isomorphism, Equivalence, and Adjunction”

Limits and co-Limits: Some Cool Things

I’m not going to reiterate the definitions of limits and co-limits from the last post, so just look them up if you’re new here.  They’re not too hard. This post is mainly just about some random cool things I’ve noticed/ “remembered” / come across whilst playing with the notions of limit and co-limit in variousContinue reading “Limits and co-Limits: Some Cool Things”