Coreflectivity of E-Monads and Algebraic Hulls

Günther Richter ()
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Günther Richter: Universität Bielefeld, Fakultät für Mathematik

A chapter in Papers in Honour of Bernhard Banaschewski, 2000, pp 161-173 from Springer

Abstract: Abstract Let X be a category with a given (E,M)-factorization structure for morphisms, M ⊆ ono X. In general, an arbitrary endofunctor T of X fails badly to preserve the E-class. If T carries a monad structure, then T(E) ⊆ E implies that the corresponding category of Eilenberg—Moorealgebras admits (E, M)-factorizations and vice versa. In order to get T as close as possible to this nice algebraic behaviour, a couniversal modification T̂ ↪ T with T̂ (E) ⊆ E is constructed in two different ways using mild and natural assumptions on E and M, respectively. T inherits its monad structure from T. In case of T = UF,F ⊣ U,the Eilenberg—Moore-category of T̂ contains a universal (E, M)-algebraic hull (completion) of U [2, 3]. There are further applications to varietal hulls [4] and to function spaces.

Keywords: monads; factorizations of (homo)molphisms; varietal and algebraic hulls; function spaces.; 18A22; 18A32; 18C05; 18C15; 54B30; 54C35 (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-94-017-2529-3_9

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