  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 $Jf:F\rightarrow Sets$ where $F$ is the category with the set
of objects ${\bf N}$ 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.
