Generalized multicategories: change-of-base, embedding, and descent

• DOI: 10.48550/arxiv.2309.08084
• Publication Date: 2023-01-01
• Authors: Rui Prezado; Fernando Lucatell...
• Keywords: Monad (category theory); Base (topology); Descent (aeronautics); Adjunction

Via the adjunction $ - \boldsymbol{\cdot} 1 \dashv \mathcal V(1,-) \colon \mathsf{Span}(\mathcal V) \to V \text{-} \mathsf{Mat} and a cartesian monad T on an extensive category with finite limits, we construct \mathsf{Cat}(T,\mathcal (\overline T, V)\text{-}\mathsf{Cat} between categories of generalized enriched multicategories internal multicategories, provided satisfies suitable condition, which is satisfied by several examples. We verify, moreover, left adjoint fully faithful, preserves pullbacks, that copower functor \mathsf{Set} faithful. also apply this result to study descent theory multicategorical structures. These results are built upon base-change for which, in turn, was carried out context horizontal lax algebras arising 2-category pseudodouble categories.