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- W4386840151 abstract "Via the adjunction $ - boldsymbol{cdot} 1 dashv mathcal V(1,-) colon mathsf{Span}(mathcal V) to mathcal V text{-} mathsf{Mat} $ and a cartesian monad $ T $ on an extensive category $ mathcal V $ with finite limits, we construct an adjunction $ - boldsymbol{cdot} 1 dashv mathcal V(1,-) colon mathsf{Cat}(T,mathcal V) to (overline T, mathcal V)text{-}mathsf{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 the copower functor $ - boldsymbol{cdot} 1 colon mathsf{Set} to 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." @default.
- W4386840151 created "2023-09-19" @default.
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- W4386840151 date "2023-09-14" @default.
- W4386840151 modified "2023-09-27" @default.
- W4386840151 title "Generalized multicategories: change-of-base, embedding, and descent" @default.
- W4386840151 doi "https://doi.org/10.48550/arxiv.2309.08084" @default.
- W4386840151 hasPublicationYear "2023" @default.
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