Lawvere theory

In category theory, a Lawvere theory (named after American mathematician William Lawvere) is a category which can be considered a categorical counterpart of the notion of an equational theory.

Let ${\displaystyle \aleph _{0}}$ be a skeleton of the category FinSet of finite sets and functions. Formally, a Lawvere theory consists of a small category L with (strictly associative) finite products and a strict identity-on-objects functor ${\displaystyle I:\aleph _{0}^{\text{op}}\rightarrow L}$ preserving finite products.

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