category theory

Last updated Feb 25, 2025

• 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)