Vol. 63, No. 2, 1976

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ISSN: 0030-8730
V -localizations and V -monads. II

Harvey Eli Wolff

Vol. 63 (1976), No. 2, 579–589

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 Tis induced on A1] and the canonical projection B-functor Φ : A A1] induces a B-functor L : AT A1]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.

Mathematical Subject Classification 2000
Primary: 18D20
Received: 4 August 1975
Revised: 31 December 1975
Published: 1 April 1976
Harvey Eli Wolff