Geodesic
Higher weak (co)limits, adjoint functor theorems, and higher Brown representability
Documenta mathematica, Tome 27 (2022), pp. 1369-1420 Cet article a éte moissonné depuis la source EMS Press

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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 ∞-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 ∞-categories if n≥2, and the homotopy n-categories of presentable stable ∞-categories for any n≥1.
DOI : 10.4171/dm/900
Classification : 18G80, 18N60, 55P99, 55U35
Mots-clés : adjoint functor theorem, Brown representability, higher categories 
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     author = {Hoang Kim Nguyen and George Raptis and Christoph Schrade},
     title = {Higher weak (co)limits, adjoint functor theorems, and higher {Brown} representability},
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     year = {2022},
     volume = {27},
     doi = {10.4171/dm/900},
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Hoang Kim Nguyen; George Raptis; Christoph Schrade. Higher weak (co)limits, adjoint functor theorems, and higher Brown representability. Documenta mathematica, Tome 27 (2022), pp. 1369-1420. doi: 10.4171/dm/900

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