Николай Иваныч (nivanych) wrote in category_theory,
Николай Иваныч
nivanych
category_theory

Lawvere theories and Jf-relative monads

[by oskar_808]
Lawvere theories and Jf-relative monads
Vladimir Voevodsky
http://arxiv.org/abs/1601.02158
In this paper we provide a detailed construction of an equivalence between the category of Lawvere theories and the category of relative monads on the obvious functor
J f : F → Sets
where F is the category with the set of objects N and morphisms being the functions between the standard finite sets of the corresponding cardinalities.
The methods of this paper are fully constructive and it should be formalizable in the Zermelo-Fraenkel theory without the axiom of choice and the excluded middle.
It is also easily formalizable in the UniMath.
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