The mathematics of mathematics — made visual through 41 interactive demonstrations.
See also: Algebraic Geometry for schemes-as-functors and representable functors in practice, Algebraic Topology for the homology and homotopy functors that built the field, and Representation Theory for functors from groups to vector spaces.
The atoms of category theory: objects, arrows, and hom-sets
How arrows compose, identity morphisms, and associativity
Set, Grp, Top, Vect, and poset categories in action
Structure-preserving maps between categories
Morphisms between functors and the naturality square
Universal properties, Cartesian products, and disjoint unions
Cones, pullbacks, equalizers, and the limit zoo
The most important concept: free-forgetful pairs and hom-set bijections
You are what you relate to: representable functors and presheaves
Monads from adjunctions and the string diagram calculus