A Lawvere theory is a small category with finite products generated by one object: every object is a finite power . A model in a finite-product category is a finite-product-preserving functor from the theory.
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Lawvere theory is a concept in category theory and is named after the mathematician William Lawvere, who introduced it in the context of topos theory and categorical logic. A Lawvere theory is essentially a generalization of a model of a universal algebra, and it provides a framework for discussing algebraic structures in a categorical manner. ### Definition: A **Lawvere theory** is typically defined as a category \(\mathcal{L}\) that satisfies certain properties.