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Pro-Categories and Multiadjoint Functors

Published online by Cambridge University Press:  20 November 2018

Walter Tholen
Walter Tholen*
Affiliation:
York University, Downsview, Ontario
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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]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 1 , 01 February 1984 , pp. 144 - 155
Copyright
Copyright © Canadian Mathematical Society 1984

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