Category Theory

• category theory formalizes mathematical structures (e.g. algebraic structures, topological structures, differential structures, etc) and their concepts in terms of a labeled directed graph (called a category) containing:
  • a set of nodes (mathematical objects)
  • a set of labeled directed edges (arrows or morphisms)
• category theory seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent
• informally, category theory is a general theory of functions

• a category has two basic properties:

  • the ability to compose the arrows associatively
  • the existence of an identity arrow for each object
    

Category Theory - Subpages

• Adjunction
• Category/Categories
• Duality
• Functors
• Natural Transformations - Natural Isomorphisms - Natural Equivalence - Isomorphism of Functors - Infranatural Transformations
• Naturality

• Mathematical Object
• Morphisms - Homomorphic/Homomorphisms (Isomorphic/Isomorphisms - Monomorphic/Monomorphisms/Injective - Epimorphic/Epimorphisms/Surjective - Endomorphic/Endomorphisms - Automorphic/Automorphisms)

Resources

• A Gentle Introduction to Category Theory.pdf
• Category Theory in Context - textbook ~ Emily Riehl
• ∞-Category Theory for Undergraduates ~ Emily Riehl
  
• Oliver Lugg - A Sensible Introduction to Category Theory

TODO

• read https://en.wikipedia.org/wiki/Category_theory#Basic_concepts
• read https://plato.stanford.edu/entries/category-theory/#GeneDefiExamAppl