The Enriched Grothendieck Construction
| Autor: | Liang Ze Wong, Jonathan Beardsley |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
General Mathematics
010102 general mathematics Coproduct Monoidal category Mathematics - Category Theory Disjoint sets 01 natural sciences 18D30 (Primary) 18D20 (Secondary) 55U40 Combinatorics Cartesian closed category Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Category Theory (math.CT) 010307 mathematical physics 0101 mathematics Equivalence (formal languages) Grothendieck construction Mathematics |
| Popis: | We define and study opfibrations of $V$-enriched categories when $V$ is an extensive monoidal category whose unit is terminal and connected. This includes sets, simplicial sets, categories, or any locally cartesian closed category with disjoint coproducts and connected unit. We show that for an ordinary category $B$, there is an equivalence of 2-categories between $V$-enriched opfibrations over the free $V$-category on $B$, and pseudofunctors from $B$ to the 2-category of $V$-categories. This generalizes the classical ($Set$-enriched) Grothendieck correspondence. Final version to appear in Advances in Mathematics, minor changes after further refereeing, 30 pages |
| Databáze: | OpenAIRE |
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