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Calculating limits and colimits in pro-categories

Daniel C. Isaksen (2002)

Fundamenta Mathematicae

We present some constructions of limits and colimits in pro-categories. These are critical tools in several applications. In particular, certain technical arguments concerning strict pro-maps are essential for a theorem about étale homotopy types. We also correct some mistakes in the literature on this topic.

Cancellative actions

Pierre Antoine Grillet (2003)

Commentationes Mathematicae Universitatis Carolinae

The following problem is considered: when can the action of a cancellative semigroup S on a set be extended to a simply transitive action of the universal group of S on a larger set.

Cartan-Eilenberg projective, injective and flat complexes

Xiaorui Zhai, Chunxia Zhang (2016)

Czechoslovak Mathematical Journal

Let R be an associative ring with identity and a class of R -modules. In this article: we first give a detailed treatment of Cartan-Eilenberg complexes and extend the basic properties of the class to the class CE ( ). Secondly, we study and give some equivalent characterizations of Cartan-Eilenberg projective, injective and flat complexes which are similar to projective, injective and flat modules, respectively. As applications, we characterize some classical rings in terms of these complexes,...

Cartesian bicategories. II.

Carboni, A., Kelly, G.M., Walters, R.F.C., Wood, R.J. (2007)

Theory and Applications of Categories [electronic only]

Cartesian closed hull for (quasi-)metric spaces (revisited)

Mark Nauwelaerts (2000)

Commentationes Mathematicae Universitatis Carolinae

An existing description of the cartesian closed topological hull of p MET , the category of extended pseudo-metric spaces and nonexpansive maps, is simplified, and as a result, this hull is shown to be a special instance of a “family” of cartesian closed topological subconstructs of p q s MET , the category of extended pseudo-quasi-semi-metric spaces (also known as quasi-distance spaces) and nonexpansive maps. Furthermore, another special instance of this family yields the cartesian closed topological hull of...

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