Background
Basic concepts
equivalences in/of $(\infty,1)$-categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
Compactly assembled (∞,1)-categories are characterized among presentable (∞,1)-categories by the following equivalent conditions (due to Clausen and Lurie):
They are retracts in the (∞,1)-category of presentable (∞,1)-categories and left adjoints of compactly generated (∞,1)-categories.
Small (∞,1)-limits distribute over (∞,1)-filtered (∞,1)-colimits.
The colimit (∞,1)-functor $Ind(C)\to C$ admits a left adjoint.
See Krause & Nikolaus 2024, Thm 2.2.11 for a few other conditions.
(∞,1)-sheaves of ∞-groupoids on a locally compact Hausdorff topological space form a compactly assembled (∞,1)-category.
Last revised on March 19, 2024 at 06:15:50. See the history of this page for a list of all contributions to it.