For a symmetric
monoidal closed category B satisfying certain completeness conditions, consider
a B-category A, a subcategory Σ of A which admits a B-calculus of left
fractions, and a B-monad T = (T,η,μ) on A. Suppose T is compatible with Σ
so that a B-monad T′ is induced on A[Σ−1] and the canonical projection
B-functor Φ : A → A[Σ−1] induces a B-functor L : AT→ A[Σ−1]T′ on the
B-categories of Eilenberg-Moore algebras. Suppose that Σ is conice and AT has
coequalizers. We prove that, if L preserves coequalizers (which is true in the case
where T preserves coequalizers), then L is the canonical projection for the
B-localization of a subcategory of BT which admits a B-calculus of left
fractions.
