Cartesian fibrations of (∞, 2)-categories

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00603994" target="_blank" >RIV/67985840:_____/24:00603994 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.2140/agt.2024.24.4731" target="_blank" >https://doi.org/10.2140/agt.2024.24.4731</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2140/agt.2024.24.4731" target="_blank" >10.2140/agt.2024.24.4731</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cartesian fibrations of (∞, 2)-categories

Popis výsledku v původním jazyce

We introduce four variance flavors of (co)cartesian fibrations of infinity-bicategories with infinity-bicategorical fibers, in the framework of scaled simplicial sets. Given a map p:E -> B of infinity-bicategories, we define p-(co)cartesian arrows and inner/outer triangles by means of lifting properties against p, leading to a notion of 2-inner/outer (co)cartesian fibrations as those maps with enough (co)cartesian lifts for arrows and enough inner/outer lifts for triangles, together with a compatibility property with respect to whiskerings in the outer case. By doing so, we also recover in particular the case of infinity-bicategories fibered in infinity-categories studied in previous work. We also prove that equivalences of such fibrations can be tested fiberwise. As a motivating example, we show that the domain projection d:Fun(gr)(Delta(1),C)-> C is a prototypical example of a 2-outer cartesian fibration, where Fun(gr)(X,Y) denotes the infinity-bicategory of functors, lax natural transformations and modifications. We then define 2-inner and 2-outer flavors of (co)cartesian fibrations of categories enriched in infinity-categories, and we show that a fibration p:E -> B of such enriched categories is a (co)cartesian 2-inner/outer fibration if and only if the corresponding map Nsc(p):N-sc epsilon ->(NB)-B-sc is a fibration of this type between infinity-bicategories.

Název v anglickém jazyce

Cartesian fibrations of (∞, 2)-categories

Popis výsledku anglicky

We introduce four variance flavors of (co)cartesian fibrations of infinity-bicategories with infinity-bicategorical fibers, in the framework of scaled simplicial sets. Given a map p:E -> B of infinity-bicategories, we define p-(co)cartesian arrows and inner/outer triangles by means of lifting properties against p, leading to a notion of 2-inner/outer (co)cartesian fibrations as those maps with enough (co)cartesian lifts for arrows and enough inner/outer lifts for triangles, together with a compatibility property with respect to whiskerings in the outer case. By doing so, we also recover in particular the case of infinity-bicategories fibered in infinity-categories studied in previous work. We also prove that equivalences of such fibrations can be tested fiberwise. As a motivating example, we show that the domain projection d:Fun(gr)(Delta(1),C)-> C is a prototypical example of a 2-outer cartesian fibration, where Fun(gr)(X,Y) denotes the infinity-bicategory of functors, lax natural transformations and modifications. We then define 2-inner and 2-outer flavors of (co)cartesian fibrations of categories enriched in infinity-categories, and we show that a fibration p:E -> B of such enriched categories is a (co)cartesian 2-inner/outer fibration if and only if the corresponding map Nsc(p):N-sc epsilon ->(NB)-B-sc is a fibration of this type between infinity-bicategories.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Algebraic and Geometric Topology

ISSN

1472-2739

e-ISSN

1472-2739

Svazek periodika

24

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

48

Strana od-do

4731-4778

Kód UT WoS článku

001388891700001

EID výsledku v databázi Scopus

2-s2.0-85214898541