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On the two definitions of Ho(pro C). (English) Zbl 0647.18008

In this note it is shown that the two constructions of a homotopy procategory given by the author [Math. Z. 140, 1-21 (1974; Zbl 0275.55022)] and by D. A. Edwards and H. M. Hastings [Čech and Steenrod homotopy theories with applications to geometric topology (1976; Zbl 0334.55001)] yield isomorphic categories. This implies that the Edwards-Hastings homotopy procategory and the Lisitsa-Mardešić coherent prohomotopy category [Yu. T. Lisitsa and S. Mardešić, Glasnik Mat., III. Ser. 19(39), 335-399 (1984; Zbl 0553.55009)] are equivalent.
Reviewer: K.H.Kamps

MSC:

18G55 Nonabelian homotopical algebra (MSC2010)
55U35 Abstract and axiomatic homotopy theory in algebraic topology
55P55 Shape theory
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References:

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