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) -- https://www.quora.com/In-category-theory-what-is-an-intuitive-explanation-of-the-concept-of-natural-transformation https://www.math3ma.com/blog/what-is-a-natural-transformation
  6. Functors, faithful, forgetful, concrete categories
  7. Generalised elements (motivation from prob theory), object characterised by its properties, Yoneda lemma, its corollaries -- https://www.math3ma.com/blog/the-yoneda-embedding https://www.math3ma.com/blog/the-sierpinski-space-and-its-special-property
  8. Stuff, structure, property; https://ncatlab.org/nlab/show/space+and+quantity
  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

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