Geodesic
Pushouts of Dwyer maps are (∞,1)–categorical
Hackney, Philip1 ; Ozornova, Viktoriya2 ; Riehl, Emily3 ; Rovelli, Martina4
1 Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, United States
2 Max Planck Institute for Mathematics, Bonn, Germany
3 Department of Mathematics, Johns Hopkins University, Baltimore, MD, United States
4 Department of Mathematics and Statistics, University of Massachusetts at Amherst, Amherst, MA, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2171-2183

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

The inclusion of 1–categories into (∞,1)–categories fails to preserve colimits in general, and pushouts in particular. We observe that if one functor in a span of categories belongs to a certain previously identified class of functors, then the 1–categorical pushout is preserved under this inclusion. Dwyer maps, a kind of neighborhood deformation retract of categories, were used by Thomason in the construction of his model structure on 1–categories. Thomason previously observed that the nerves of such pushouts have the correct weak homotopy type. We refine this result and show that the weak homotopical equivalence is a weak categorical equivalence. We also identify a more general class of functors along which 1–categorical pushouts are (∞,1)–categorical.

DOI : 10.2140/agt.2024.24.2171
Keywords: Dwyer map, nerve functor, $(\infty,1)$–category, simplicial category, quasicategory

Hackney, Philip 1 ; Ozornova, Viktoriya 2 ; Riehl, Emily 3 ; Rovelli, Martina 4

1 Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, United States
2 Max Planck Institute for Mathematics, Bonn, Germany
3 Department of Mathematics, Johns Hopkins University, Baltimore, MD, United States
4 Department of Mathematics and Statistics, University of Massachusetts at Amherst, Amherst, MA, United States 
@article{10_2140_agt_2024_24_2171,
     author = {Hackney, Philip and Ozornova, Viktoriya and Riehl, Emily and Rovelli, Martina},
     title = {Pushouts of {Dwyer} maps are (\ensuremath{\infty},1){\textendash}categorical},
     journal = {Algebraic and Geometric Topology},
     pages = {2171--2183},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2024},
     doi = {10.2140/agt.2024.24.2171},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2171/}
}
TY  - JOUR
AU  - Hackney, Philip
AU  - Ozornova, Viktoriya
AU  - Riehl, Emily
AU  - Rovelli, Martina
TI  - Pushouts of Dwyer maps are (∞,1)–categorical
JO  - Algebraic and Geometric Topology
PY  - 2024
SP  - 2171
EP  - 2183
VL  - 24
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2171/
DO  - 10.2140/agt.2024.24.2171
ID  - 10_2140_agt_2024_24_2171
ER  - 
%0 Journal Article
%A Hackney, Philip
%A Ozornova, Viktoriya
%A Riehl, Emily
%A Rovelli, Martina
%T Pushouts of Dwyer maps are (∞,1)–categorical
%J Algebraic and Geometric Topology
%D 2024
%P 2171-2183
%V 24
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2171/
%R 10.2140/agt.2024.24.2171
%F 10_2140_agt_2024_24_2171
Hackney, Philip; Ozornova, Viktoriya; Riehl, Emily; Rovelli, Martina. Pushouts of Dwyer maps are (∞,1)–categorical. Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2171-2183. doi: 10.2140/agt.2024.24.2171

Cité par Sources :