J 2024

Discrete equational theories

ROSICKÝ, Jiří

Basic information

Original name

Discrete equational theories

Authors

ROSICKÝ, Jiří (203 Czech Republic, guarantor, belonging to the institution)

Edition

Mathematical Structures in Computer Science, Cambridge, Cambridge University Press, 2024, 0960-1295

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Impact factor

Impact factor: 0.500 in 2022

Organization unit

Faculty of Science

UT WoS

001147013000001

Keywords in English

Enriched equational theory; enriched monad; Birkhoff subcategory

Tags

Tags

International impact, Reviewed
Změněno: 8/2/2024 08:59, Mgr. Marie Šípková, DiS.

Abstract

V originále

On a locally $\lambda$-presentable symmetric monoidal closed category $\mathcal {V}$, $\lambda$-ary enriched equational theories correspond to enriched monads preserving $\lambda$-filtered colimits. We introduce discrete $\lambda$-ary enriched equational theories where operations are induced by those having discrete arities (equations are not required to have discrete arities) and show that they correspond to enriched monads preserving preserving $\lambda$-filtered colimits and surjections. Using it, we prove enriched Birkhof-type theorems for categories of algebras of discrete theories. This extends known results from metric spaces and posets to general symmetric monoidal closed categories.

Links

GA22-02964S, research and development project
Name: Obohacené kategorie a jejich aplikace (Acronym: ECATA)
Investor: Czech Science Foundation