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Coreflectivity of E-Monads and Algebraic Hulls

In: Papers in Honour of Bernhard Banaschewski

Author

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  • Günther Richter

    (Universität Bielefeld, Fakultät für Mathematik)

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.

Suggested Citation

  • Günther Richter, 2000. "Coreflectivity of E-Monads and Algebraic Hulls," Springer Books, in: Guillaume Brümmer & Christopher Gilmour (ed.), Papers in Honour of Bernhard Banaschewski, pages 161-173, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2529-3_9
    DOI: 10.1007/978-94-017-2529-3_9
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