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027 MOC Category Theory

027 MOC Category Theory

Jul 28, 20231 min read

  • moc

up:: 020 MOC Mathematics

Category Theory has been half-jokingly called “abstract nonsense” for quite a while now. It can be seen less harshly when talking about its role in abstraction, which is undoubtedly what Mathematics is all about, in the grand scheme of things. A great video that elucidates this is The Mathematician’s Weapon | Category Theory and Why We Care 1.0, from channel Eyesomorphic.

Topics

  • Category
  • Hom-Set
  • Monomorphism
    • An injective function is a monomorphism in the category Set
  • Epimorphism
    • A surjective function is an epimorphism in the category Set
  • Opposite Category
  • Functor
    • Contravariant Functor
    • Group Actions can be seen as functors
    • Groups can be seen as automorphisms in single-element categories
  • Natural Transformation
  • Initial Object
  • Terminal Object
    • A terminal object is isomorphic to an initial object if there is a morphism from T to I
  • Zero Object
  • Product (Category)
  • Colimit
  • Yoneda Lemma
  • Sheaf
  • Presheaf
  • Topos

Category Examples

  • Single-Element Category
  • Groupoid
  • Set Category
  • Vect Category

Graph View

  • Topics
  • Category Examples

Backlinks

  • 020 MOC Mathematics
  • A terminal object is isomorphic to an initial object if there is a morphism from T to I
  • Category
  • Initial Object
  • Opposite Category
  • Notas para Economia Matemática
  • Product (Category)
  • Terminal Object
  • Yoneda Lemma
  • Zero Object
  • Digital Garden Entrance

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