Original Articles

ON ADJUNCTIONS INDUCING THE SAME MONAD

Published in: Quaestiones Mathematicae
Volume 7 , issue 2 , 1984 , pages: 179–201

DOI: 10.1080/16073606.1984.9632329

Author(s): Manuela Sobral Departamento de Matematica, PORTUGAL

Keywords: 18C99 , 18A40.

Abstract

Consider an adjunction <F,U;n,c>: K. → A, T = <T,n,u> the monad it induces in K and ø: A → K^T the comparison functor, K^T being the category of T-algebras. By ø*: Proj U → Proj U^T we denote the restriction and co-restriction of ø to the subcategories of U-projective and U^T -projective objects, respectively. In this paper we deal with the following problem, raised by R.-E. Hoffmann in [5] 1.16 (b):

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