Displaying similar documents to “Lusternik-Schnirelmann category and minimal coverings with contractible sets.”

Fibrations in the Category of Absolute Neighborhood Retracts

Takahisa Miyata (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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The category Top of topological spaces and continuous maps has the structures of a fibration category and a cofibration category in the sense of Baues, where fibration = Hurewicz fibration, cofibration = the usual cofibration, and weak equivalence = homotopy equivalence. Concentrating on fibrations, we consider the problem: given a full subcategory 𝓒 of Top, is the fibration structure of Top restricted to 𝓒 a fibration category? In this paper we take the special case where 𝓒 is the...

Reedy categories which encode the notion of category actions

Julia E. Bergner, Philip Hackney (2015)

Fundamenta Mathematicae

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We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new...

Calculating limits and colimits in pro-categories

Daniel C. Isaksen (2002)

Fundamenta Mathematicae

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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.