Batanin, M. A. Coherent categories with respect to monads and coherent prohomotopy theory. (English) Zbl 0793.18005 Cah. Topologie Géom. Différ. Catég. 34, No. 4, 279-304 (1993). It is well known that various important categories are Kleisli categories for monads in enriched settings. The work of J.-M. Cordier [Prépublication, Amiens, 1985; and Cah. Topologie Géom. Différ. Catégoriques 30, 257-275 (1989; Zbl 0679.55006)] suggests that the category introduced by R. M. Vogt [Math. Z. 134, 11-53 (1973; Zbl 0276.55006)] consisting of homotopy coherent diagrams of spaces and homotopy classes of homotopy coherent maps between them, could be described somewhat in this way. In this paper, the author shows how there is a general construction linking constructions of coherent homotopy categories in various contexts with Kleisli constructions on the unlocalised homotopy category. In particular this is applied to show the equivalence of coherent prohomotopy as introduced by Lisica and Mardešić, with a Kleisli category for a monad on \(\pi(\text{pro- }K)\). The generality of the construction allows the author to obtain several other related results including some on \(R\)-completions. Reviewer: T.Porter (Bangor) Cited in 2 ReviewsCited in 13 Documents MSC: 18D20 Enriched categories (over closed or monoidal categories) 55U35 Abstract and axiomatic homotopy theory in algebraic topology Keywords:Kleisli categories; homotopy classes; coherent homotopy categories; unlocalised homotopy category; coherent prohomotopy Citations:Zbl 0679.55006; Zbl 0276.55006 PDFBibTeX XMLCite \textit{M. A. Batanin}, Cah. Topologie Géom. Différ. Catégoriques 34, No. 4, 279--304 (1993; Zbl 0793.18005) Full Text: Numdam EuDML References: [1] 1 Batanin M.A. , About the coherent prohomotopy category of Lisica-Mardesič and generalized Steenrod homology theories (Russian) , Preprint 1986 . 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