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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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