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Strong functors on many-sorted sets

Paul B. Levy (2019)

Commentationes Mathematicae Universitatis Carolinae

We show that, on a category of many-sorted sets, the only functors that admit a cartesian strength are those that are given componentwise.

Structures d’asphéricité, foncteurs lisses, et fibrations

Georges Maltsiniotis (2005)

Annales mathématiques Blaise Pascal

Le but de cet article est de généraliser la théorie des foncteurs lisses de Grothendieck afin d’inclure dans ce cadre la théorie des catégories fibrées. On obtient en particulier une nouvelle caractérisation des catégories fibrées.

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 → [ 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...

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