Category theory

  1. Introduction to category theory: a second abstraction
  2. Abstracting some categorical definitions
  3. Abstracting our abstractions: limits of cones, universal properties  + examples
  4. Incredible duals
  5. Anti-isomorphisms, natural isomorphisms and transformations (motivation from kernel cokernel not natural, dual not natural but double dual natural) --
  6. Functors, faithful, forgetful, concrete categories
  7. Generalised elements (motivation from prob theory), object characterised by its properties, Yoneda lemma, its corollaries --
  8. Stuff, structure, property;
  9. Theorems with our definitions: injectivity and kernels, first isomorphism theorem, rank-nullity, kernels are ideals... what special properties do we need?
  10. Studying categories with category theory

No comments:

Post a Comment