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Total Categories and Solid Functors

Published online by Cambridge University Press:  20 November 2018

Reinhard Börger  and
Walter Tholen
Reinhard Börger
Affiliation:
Fernuniversität, Hagen, Federal Republic of Germany
Walter Tholen
Affiliation:
York UniversityNorth York, Ontario
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Totality of a category as introduced by Street and Walters [17] is known to be a strong cocompleteness property (cf. also [21]) which goes far beyond ordinary (small) cocompleteness. It implies compactness in the sense of Isbell [11] and therefore hypercompleteness [7], that is: the existence of limits of all those (not necessarily small) diagrams which are not prevented from having a limit merely from size-considerations with respect to the homsets. In particular, arbitrary intersections of monomorphisms exist in a total category; which is part of Street's [16] characterization of totality and is used in establishing the interrelationship with topoi (cf. also [15]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 2 , 01 April 1990 , pp. 213 - 229
Copyright
Copyright © Canadian Mathematical Society 1990

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