lean2/hott/algebra/category/constructions/constructions.md

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algebra.category.constructions

Common categories and constructions on categories. The following files are in this folder.

  • functor : Functor category
  • opposite : Opposite category
  • hset : Category of sets. Includes proof that it is complete and cocomplete
  • sum : Sum category
  • product : Product category
  • comma : Comma category
  • cone : Cone category

Discrete, indiscrete or finite categories:

  • finite_cats : Some finite categories, which are diagrams of common limits (the diagram for the pullback or the equalizer). Also contains a general construction of categories where you give some generators for the morphisms, with the condition that you cannot compose two of thosex
  • discrete
  • indiscrete
  • terminal
  • initial

Non-basic topics:

  • functor2 : showing that the functor category has (co)limits if the codomain has them.