Mario Román

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category theory

category theory

May 08, 20251 min read

  • index

Topics.

  • monoidal category
  • polycategory
  • multicategory
  • Functor
  • profunctor
  • Markov category
  • bicategory, monoidal bicategory, and higher categories.
  • monoidal contexts, optics,
  • non-associative category
  • double category
    • multicategory - promonoidal category, produoidal category
  • Type theory
    • Type theory for symmetric monoidal categories

Variants of monoidal categories.

  • multicategory
  • multicategory - promonoidal category
  • duoidal category
  • premonoidal category
  • Freyd category
  • effectful category
  • linearly distributive category
  • polycategory
  • monoidal bicategory
  • copy-discard category
  • distributive category
  • distributive copy-discard category
  • distributive copy-discard-uniform category

Formal category theory.

  • Functor
  • natural transformation
  • bicategory
  • displayed category
  • double category
  • enriched category

References.

  • Categories for the Working Mathematician (MacLane)

Graph View

Backlinks

  • Adjunction
  • categorical logic
  • Monoid theorist
  • monoidal natural transformation
  • profunctor
  • quotients and relations
  • the problem is not to find an internal language, it is to find a sharp one

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