Cartesian fibrations of (∞, 2)-categories
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Cartesian fibrations of (∞, 2)-categories
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Algebraic and Geometric Topology
ISSN
1472-2739
e-ISSN
1472-2739
Volume of the periodical
24
Issue of the periodical within the volume
9
Country of publishing house
GB - UNITED KINGDOM
Number of pages
48
Pages from-to
4731-4778
UT code for WoS article
001388891700001
EID of the result in the Scopus database
2-s2.0-85214898541