modern category theory



modern category theory

For DAG:

Topics

  • Constructions of new categories:
    • slice category
    • comma category
  • Structure on categories:
  • Extending functors:
    • Kan extension
    • coend
    • Day convolution
  • Structure on functors
    • continuous functor
    • continuous functor
  • span
  • Object function of an equivalence of categories?

Internal Objects

  • monoid object
  • Unsorted/group object
  • ring object
  • module object
  • vector space object
  • algebra object
  • simplicial object

Monoidal

  • dualizable object of a category
  • invertible object of a category
  • center in a category
  • compact object of a category
  • Generators of a category
  • linear category
  • fiber functor
  • tannakian
  • filtered objects of a category
  • graded objects of a category
  • Calabi-Yau object of a category

Homotopy

^72ca2f - homotopy colimit - homotopy quotient - homotopy fixed points

Higher Cats

  • higher category
  • infinity categories
  • stable infinity category
  • presentable category
  • DG category
  • graded category
  • whiskering

Representation Theory

  • blocks of a category
  • semiorthogonal decomposition
  • quivers
  • semisimple category
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