@UNPUBLISHED{publication1,
title = "Generalized multicategories: change-of-base, embedding, and descent",
author = "{PREZADO, Rui} and {LUCATELLI NUNES, Fernando}",
year = "2023-09-14",
abstract = "Via the adjunction \&\#8722;· 1 \&\#8867; $\backslash$( $\backslash$mathcal V $\backslash$)(1,\&\#8722;) : *Span*($\backslash$( $\backslash$mathcal V $\backslash$)) \&\#8594; $\backslash$( $\backslash$mathcal V $\backslash$)-**Mat** and a cartesian monad *T* on an extensive category\ $\backslash$( $\backslash$mathcal V $\backslash$) with finite limits, we construct an adjunction \&\#8722;·1 \&\#8867; $\backslash$( $\backslash$mathcal V $\backslash$)(1,\&\#8722;) : *Cat*(T, $\backslash$( $\backslash$mathcal V $\backslash$)) \&\#8594; (T, $\backslash$( $\backslash$mathcal V $\backslash$))-*Cat* between categories of generalized enriched multicategories and generalized internal multicategories , provided the monad *T* satisfies a suitable condition, which is satisfied by several examples. We verify, moreover, the left adjoint is fully faithful, and preserves pullbacks, provided that \&\#8722; · 1: *Set* \&\#8594;\ $\backslash$( $\backslash$mathcal V $\backslash$) is fully faithful. We also apply this result to study descent theory of generalized enriched multicategorical structures. These results are built upon the study of base-change for generalized multicategories, which, in turn, was carried out in the context of categories of horizontal lax algebras arising out of a monad in a suitable 2-category of pseudodouble categories.

",
url = "http://www.mat.uc.pt/preprints/eng\_2023.html",
note = ""
}