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5
votes
What algebraic structure controls endomorphisms of algebras over a Lawvere theory
The answer is yes. For every Lawvere theory $T$, there is a Lawvere theory whose algebras are endomorphisms of $T$-algebras. I'll show this by passing through the category of PROPs.
Note first that ev …
1
vote
Category of multisorted Lawvere's theories
A definition can be found in 4.1 (page 8) of Charles Rezk's paper "Every Homotopy Theory of Simplicial Algebras Admits a Proper Model." The category of $J$-sorted theory is the category of monoids in …