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A Finite Algebraic Presentation of Lawvere Theories in the Object-Classifier Topos
Theory and applications of categories, Lawvere Festschrift, Tome 43 (2025), pp. 181-195 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.
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Classification : 08C05, 18C10, 18C15, 18C40, 18E99
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 
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     author = {Marcelo Fiore and Sanjiv Ranchod},
     title = {A {Finite} {Algebraic} {Presentation} of {Lawvere} {Theories}  in the
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     journal = {Theory and applications of categories},
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Marcelo Fiore; Sanjiv Ranchod. A Finite Algebraic Presentation of Lawvere Theories  in the
  Object-Classifier Topos. Theory and applications of categories, Lawvere Festschrift, Tome 43 (2025), pp. 181-195. http://geodesic.mathdoc.fr/item/TAC_2025_43_a6/