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Displaying 101 – 118 of 118

Sur les catégories complètes

R. Pupier (1965)

Publications du Département de mathématiques (Lyon)

Technique de descente et théorèmes d'existence en géométrie algébriques. II. Le théorème d'existence en théorie formelle des modules

Alexander Grothendieck (1958/1960)

Séminaire Bourbaki

The category of uniform spaces as a completion of the category of metric spaces

Jiří Adámek, Jan Reiterman (1992)

Commentationes Mathematicae Universitatis Carolinae

A criterion for the existence of an initial completion of a concrete category $𝐊$ universal w.r.tḟinite products and subobjects is presented. For $𝐊 =$ metric spaces and uniformly continuous maps this completion is the category of uniform spaces.

The structure of initial completions

J. Adámek, H. Herrlich, G. E. Strecker (1979)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Théories de catégories

J. Penon (1979)

Diagrammes

Topological Space Objects in a Topos II: ...-Completeness and ...-Cocompleteness.

Lawrence Neff Stout (1975)

Manuscripta mathematica

Topologically-algebraic structure functors full reflective or coreflective restrictions of semitopological functors

Manfred B. Wischnewsky (1979)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Totality of colimit closures

Reinhard Börger, Walter Tholen (1991)

Commentationes Mathematicae Universitatis Carolinae

Adámek, Herrlich, and Reiterman showed that a cocomplete category $𝒜$ is cocomplete if there exists a small (full) subcategory $ℬ$ such that every $𝒜$ -object is a colimit of $ℬ$ -objects. The authors of the present paper strengthened the result to totality in the sense of Street and Walters. Here we weaken the hypothesis, assuming only that the colimit closure is attained by transfinite iteration of the colimit closure process up to a fixed ordinal. This requires some investigations on generalized notions...

Totality of product completions

Jiří Adámek, Lurdes Sousa, Walter Tholen (2000)

Commentationes Mathematicae Universitatis Carolinae

Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. We introduce the notion of multitotal category $𝒜$ by asking the Yoneda embedding $𝒜 \to [𝒜^{o p}, 𝒮 e t]$ to be right multiadjoint and prove that this property is equivalent to totality of the formal product completion $Π 𝒜$ of $𝒜$ . We also characterize multitotal categories with various types of generators; in particular, the existence of dense generators is inherited by the formal product...