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What algebraic structure controls endomorphisms of algebras over a Lawvere theory

Given a Lawvere theory $T,$ is it possible to describe a Lawvere theory $\textrm{End}(T)$ such that $\textrm{End}(T)$-algebras describe "endomorphisms of $T$-algebras"? In other words, what can be sai …
Grisha Taroyan's user avatar