# Duoidal category

*Related.*

- normal duoidal category
- Virtual duoidal category
- produoidal category
- Duoids bimonoids in a duoidal
- Strings for duoidal categories
- Compositional dependencies with duoidals
- Two-sided duoidal duality
- Coherence for duoidals, wrong statement
- Conjecture - Every duoidal embeds into an adjoint pseudomonoid
- Signalling structure of process theories
- Eckmann-Hilton intuition for duoidal categories
- Strict duoidal category
- Old - Duoidal category

*References*

- Commutativity (Garner, Lopez Franco, 2015)
- Duoidal Structures for Compositional Dependence (Shapiro, Spivak, 2022)
- A coherence theorem for duoidal categories can be found in the work of (Aguiar, Mahahan, 2009). One needs to be careful, though, because it looks wrong as stated.

#definition