Internal categories in a left exact cosimplicial category.

Pataraia, D.

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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 $𝒜 \to [𝒜^{o p}, 𝒮 e t]$ 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...