Geodesic
Higher weak (co)limits, adjoint functor theorems, and higher Brown representability
Documenta mathematica, Tome 27 (2022), pp. 1369-1420.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove general adjoint functor theorems for weakly (co)complete $n$-categories. This class of $n$-categories includes the homotopy $n$-categories of (co)complete $\infty$-categories, so these $n$-categories do not admit all small (co)limits in general. We also introduce Brown representability for (homotopy) $n$-categories and prove a Brown representability theorem for localizations of compactly generated $n$-categories. This class of $n$-categories includes the homotopy $n$-categories of presentable $\infty$-categories if $n \geq 2$, and the homotopy $n$-categories of presentable stable $\infty $-categories for any $n \geq 1$.
Classification : 18N60, 55U35, 18G80, 55P99
Keywords: adjoint functor theorem, Brown representability, higher category 
@article{DOCMA_2022__27__a31,
     author = {Nguyen, Hoang Kim and Raptis, George and Schrade, Christoph},
     title = {Higher weak (co)limits, adjoint functor theorems, and higher {Brown} representability},
     journal = {Documenta mathematica},
     pages = {1369--1420},
     publisher = {mathdoc},
     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a31/}
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Nguyen, Hoang Kim; Raptis, George; Schrade, Christoph. Higher weak (co)limits, adjoint functor theorems, and higher Brown representability. Documenta mathematica, Tome 27 (2022), pp. 1369-1420. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a31/