String Diagrams for Premonoidal Categories

Fuente: arXiv
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Main Authors: Román, Mario, Sobociński, Paweł
Format: Preprint
Published: 2023
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author Román, Mario
Sobociński, Paweł
author_facet Román, Mario
Sobociński, Paweł
contents Premonoidal categories are monoidal categories without the interchange law while effectful categories are premonoidal categories with a chosen monoidal subcategory of interchanging morphisms. In the same sense that string diagrams, pioneered by Joyal and Street, are an internal language for monoidal categories, we show that string diagrams with an added "runtime object", pioneered by Alan Jeffrey, are an internal language for effectful categories and can be used as string diagrams for effectful, premonoidal, and Freyd categories.
format Preprint
id arxiv_https___arxiv_org_abs_2305_06075
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle String Diagrams for Premonoidal Categories
Román, Mario
Sobociński, Paweł
Category Theory
18M30
Premonoidal categories are monoidal categories without the interchange law while effectful categories are premonoidal categories with a chosen monoidal subcategory of interchanging morphisms. In the same sense that string diagrams, pioneered by Joyal and Street, are an internal language for monoidal categories, we show that string diagrams with an added "runtime object", pioneered by Alan Jeffrey, are an internal language for effectful categories and can be used as string diagrams for effectful, premonoidal, and Freyd categories.
title String Diagrams for Premonoidal Categories
topic Category Theory
18M30
url https://arxiv.org/abs/2305.06075