Pro-Categories and Multiadjoint Functors

Tholen, Walter

Canadian journal of mathematics, Tome 36 (1984) no. 1, pp. 144-155

Résumé

For a functor G:A→X and a class D of small categories containing the terminal category 1 we form the extension and call G right D-pro-adjoint if and only if Pro (D, G) is right adjoint. Here Pro (D, A) is the completion of Awith respect to D; it coincides with the usual pro-category of A in case D = directed sets. For this D a full embedding Gis dense in the sense of Mardešić [11] if and only if it is right D-pro-adjoint in the above sense; this has been proved recently by Stramaccia [15]. The most important example is the embedding of the homotopy category of pointed CW-complexes into the homotopy category of pointed topological spaces (cf. [2]).

Détail

DOI : 10.4153/CJM-1984-010-2

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