Displaying similar documents to “On the homology of small categories and asynchronous transition systems.”

Decompositions of the category of noncommutative sets and Hochschild and cyclic homology

Jolanta Słomińska (2003)

Open Mathematics

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In this note we show that the main results of the paper [PR] can be obtained as consequences of more general results concerning categories whose morphisms can be uniquely presented as compositions of morphisms of their two subcategories with the same objects. First we will prove these general results and then we will apply it to the case of finite noncommutative sets.

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...