Generalized Multicategories: Change-of-Base, Embedding, and Descent

Rui Prezado*, Fernando Lucatelli Nunes

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Via the adjunction -∗1⊣V(1,-):Span(V)→V-Mat and a cartesian monad T on an extensive category V with finite limits, we construct an adjunction -∗1⊣V(1,-):Cat(T,V)→(T¯,V)-Cat between categories of generalized enriched multicategories and generalized internal multicategories, provided the monad T satisfies a suitable property, which holds for several examples. We verify, moreover, that the left adjoint is fully faithful, and preserves pullbacks, provided that the copower functor -∗1:Set→V 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.

Original languageEnglish
Article number35
JournalApplied Categorical Structures
Volume32
Issue number6
DOIs
Publication statusPublished - 30 Oct 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.

Keywords

  • 18B10
  • 18B15
  • 18B50
  • 18D65
  • 18N10
  • 18N15
  • Beck-Chevalley condition
  • Double category
  • Effective descent morphisms
  • Enriched category
  • Equipment
  • Extensive category
  • Generalized multicategory
  • Grothendieck descent theory
  • Higher category theory
  • Internal category
  • Lax algebra
  • Virtual equipment

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