3 papers
math.CT2023
String Diagrams for Premonoidal Categories
Mario Román, Paweł Sobociński
Premonoidal categories are monoidal categories without the interchange law while effectful categories are premonoidal categories with a chosen monoidal subcategory of interchanging…
math.CT2023
Optics for Premonoidal Categories
James Hefford, Mario Román
We further the theory of optics or "circuits-with-holes" to encompass premonoidal categories: monoidal categories without the interchange law. Every premonoidal category gives rise…
math.CT2023
Collages of String Diagrams
Dylan Braithwaite, Mario Román
We introduce collages of string diagrams as a diagrammatic syntax for glueing multiple monoidal categories. Collages of string diagrams are interpreted as pointed bimodular profunc…