Displaying similar documents to “A categorical approach to integration.”

What are sifted colimits?

Adamek, J., Rosicky, J., Vitale, E.M. (2010)

Theory and Applications of Categories [electronic only]

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Left-Garside categories, self-distributivity, and braids

Patrick Dehornoy (2009)

Annales mathématiques Blaise Pascal

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In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the relationship between the self-distributivity law LD and braids amounts to the result that a certain category associated with LD is a left-Garside category, which projects onto the standard Garside category of braids. This approach leads to a realistic program for establishing the Embedding Conjecture of [Dehornoy,...

Totality of product completions

Jiří Adámek, Lurdes Sousa, Walter Tholen (2000)

Commentationes Mathematicae Universitatis Carolinae

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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 [ 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...