A Finite Algebraic Presentation of Lawvere Theories in the Object-Classifier Topos

Marcelo Fiore and Sanjiv Ranchod

Over the topos of sets, the notion of Lawvere theory is infinite countably-sorted algebraic but not one-sorted algebraic. Shifting viewpoint over the object-classifier topos, a finite algebraic presentation of Lawvere theories is considered.

Keywords: Lawvere theory, algebraic theory, algebraic category, equational presentation, abstract clone, simultaneous substitution, symmetric monoid, symmetric monad, symmetric distributive law, single-variable substitution, object-classifier topos

2020 MSC: 08C05, 18C10, 18C15, 18C40, 18E99

Theory and Applications of Categories, Vol. 43, 2025, No. 7, pp 181-195.

Published 2025-03-16.

http://www.tac.mta.ca/tac/volumes/43/7/43-07.pdf

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