There is but one direction, therefore, which I have to give in this part of my work, namely, that he may be able to do all this successfully, let him understand what he reads.
- Mathematical Vernacular a formal language for proofs.
- Category Theory
- Object Oriented Math, a basic introduction to certain aspects of category theory, preliminary focus on mathematical objects and structure-preserving maps between them ("morphisms").
- First Taste of Categories, where we first introduced various aspects of category theory in a more heavy duty way.
- Fun With Functors, where we introduced the notion of morphisms as mapping objects to objects, and observe that a category is an object, then ask "What's a morphism from a category to a category?"
- Classification of Morphisms, setting up the taxonomy of morphisms.
- Hierarchy of Functors, setting up the taxonomy of functors.
- Natural Question: Morphisms of Functors, a first look at natural transformations.
- Products (but not Coproducts yet), wherein we first introduce the notion of the product (but not yet the coproduct!).
- Duality Principle, one of the most important concepts involving reversing your arrows.
- Coproducts (but not Products!), wherein we first introduce the notion of the coproduct.
- Equivalence of Categories, descending the Rabbit hole of "sameness" in category theory.
- Morphisms of...Morphisms? A First Look at Slice Categories [Draft!] looking at comma categories (and slice categories) as the category of morphisms.
- More Object Orientedness, revisiting the notion of a "mathematical object" with the tools of category theory.