A copy-discard category is a symmetric monoidal category that supplies cocommutative comonoids.
Definition, in the style of comonoid supplies.
Definition, in the style of effectful categories.
- copy-discard categories are a synthetic theory of information flow
- marginal
- conditional composition
- almost-sure equality
- deterministic and total morphisms
- Markov category
- conditional
- copy-discard functor
- copy and discard monad
References
- An algebraic presentation of term graphs, via gs-monoidal categories (Corradini, Gaducci, 1999) introduces copy-discard categories as gs-categories. These are used for term graph rewriting.
- Disintegration and Bayesian Inversion via String Diagrams (Cho, Jacobs, 2017) introduces copy-discard categories by their name.
- Free GS-Monoidal Categories and Free Markov Categories (Fritz, Liang, 2023) gives discussion and a construction of the free copy-discard category over a signature.
- Supplying bells and whistles in symmetric monoidal categories (Fong, Spivak, 2020) characterizes them as the symmetric monoidal categories supplying cocommutative comonoids.
Tags: symmetric monoidal category, comonoid.