Definition. Monoidal category.
Monoidal categories are an algebraic structure for transformations that can be composed sequentially and in parallel.
Theorem. Coherence for monoidal categories.
References.
- Categories for the Working Mathematician (MacLane)
- Extracting a proof of coherence for monoidal categories from a formal proof of normalization for monoids (Beylin, Dybjer)
Definition. Cartesian monoidal categories.
- cartesian category
- cartesian categories are monoidal categories
- Fox’s theorem and cocommutativity
- Refining Fox’s Theorem
- uniform copy delete
- Cartesian by split
- Cartesian, partial and stochastic
See also
Motivating monoidal categories
- 1-Dimensional calculus
- interchange law
- Coherence for monoidal categories
- Sets is a monoidal category
- Strict monoidal categories and coherence
- Examples of monoidal category
- String diagrams for category theory
- Three notations for symmetric monoidal categories
- Lax monoidal functor
Types.
- String diagrams for monad and monad algebras
- string diagrams for bicategories
- string diagrams are two
Constructions
- Dualities
- do-notation - theory of symmetric monoidal categories
- distributive law
- String diagrams for monad and monad algebras
- Motivating bicategories
As theories of processes.
Examples
Literature.