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 language | English |
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Article number | 35 |
Journal | Applied Categorical Structures |
Volume | 32 |
Issue number | 6 |
DOIs | |
Publication status | Published - 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