Generalized multicategories: change-of-base, embedding, and descent (Preprint)

  <Reference List>
Type: Preprint
National /International: International
Title: Generalized multicategories: change-of-base, embedding, and descent
Publication Date: 2023-09-14
Authors: - Rui Rodrigues de Abreu Fernandes Prezado
- Fernando Lucatelli Nunes

Via the adjunction −· 1 ⊣ \( \mathcal V \)(1,−) : Span(\( \mathcal V \)) → \( \mathcal V \)-Mat and a cartesian monad T on an extensive category \( \mathcal V \) with finite limits, we construct an adjunction −·1 ⊣ \( \mathcal V \)(1,−) : Cat(T, \( \mathcal V \)) → (T, \( \mathcal V \))-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 − · 1: Set → \( \mathcal V \) 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.

Institution: DMUC 23-29
Online version:
Download: Not available
© Centre for Mathematics, University of Coimbra, funded by
Science and Technology Foundation
Powered by: rdOnWeb v1.4 | technical support