Work

String Diagrams for Premonoidal Categories

Year: 2025

Type: article

Abstract: 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.

Source: Logical Methods in Computer Science

DOI: 10.46298/lmcs-21(2:9)2025

Authors: Mario Román, Paweł Sobociński

Institutions: Tallinn University of Technology, University of Oxford

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: European Commission, Eesti Teadusagentuur

Awards: Automata in Learning, Interaction and Concurrency (ALICE), Artificial intelligence in cybersecurity, Cyber-security Excellence Hub in Estonia and South Moravia