18 июн. 2023 г. · An (∞,1)-category is called locally presentable if it has all small (∞,1)-colimits and its objects are presented under (∞,1)-colimits by a small set of ...

16 нояб. 2023 г. · This means that the objects of a stable ( ∞ , 1 ) (\infty,1) -category are stable in the sense of stable homotopy theory: they behave as if ... Definition · Constructions in stable ∞ \infty... · Properties

4 окт. 2019 г. · A presentable (∞−)category is not a presentable object in the category of categories. Rather, the objects of the category are presentable, and ... Foundations and contradictions of Scholze's work - MathOverflow When is a stable ∞-category the stabilization of an ∞-topos? Compact generation of the infinity category of stable infinity ... Другие результаты с сайта mathoverflow.net

23 мая 2017 г. · While the definition of a stable ∞-category only uses fibers and cofibers, stable ∞-categories actually admit finite limits and colimits. ...

9 авг. 2006 г. · This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is ...

Let C be a presentable pointed ∞-category, and let Sp≤1(C) be the full subcategory of Sp(C) spanned by those objects such that Ω∞(X) is a final object of C.

A stable ∞-category admits finite limits and colimits, and a commutative square in which is a pullback square if and only if it is a pushout square.

In particular this implies that the ∞-category of spectra Sp is presentable. In fact when restricting to presentable ∞-categories we get the following result.

27 нояб. 2020 г. · colimits. we can write everything in an presentable ∞-category as colimits of a small amount of objects from a small ∞-category. Example 0.23.

8 окт. 2009 г. · Let C be a presentable stable ∞-category. We will say that a t-structure on C is accessible if the subcategory C≥0 ⊆ C is presentable.