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@article{2371438,
author = {Rosický, Jiří},
article_location = {Cambridge},
article_number = {2},
doi = {http://dx.doi.org/10.1017/S096012952400001X},
keywords = {Enriched equational theory; enriched monad; Birkhoff subcategory},
language = {eng},
issn = {0960-1295},
journal = {Mathematical Structures in Computer Science},
title = {Discrete equational theories},
url = {https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science/article/discrete-equational-theories/B68D91B64C2E6EC95C441A67CD9A24A4},
volume = {34},
year = {2024}
}
TY - JOUR
ID - 2371438
AU - Rosický, Jiří
PY - 2024
TI - Discrete equational theories
JF - Mathematical Structures in Computer Science
VL - 34
IS - 2
SP - 147-160
EP - 147-160
PB - Cambridge University Press
SN - 09601295
KW - Enriched equational theory
KW - enriched monad
KW - Birkhoff subcategory
UR - https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science/article/discrete-equational-theories/B68D91B64C2E6EC95C441A67CD9A24A4
N2 - 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.
ER -
ROSICKÝ, Jiří. Discrete equational theories. \textit{Mathematical Structures in Computer Science}. Cambridge: Cambridge University Press, 2024, vol.~34, No~2, p.~147-160. ISSN~0960-1295. Available from: https://dx.doi.org/10.1017/S096012952400001X.
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