5 сент. 2010 г. · "The ∞-category of spetra is the free stable ∞-category with colimits generated by a single object". That's a nice model independent definition ...

13 окт. 2023 г. · There should also be a Proposition saying that the infinity category of dg categories is complete, which I could not find in Lurie's book ...

12 дек. 2009 г. · The slogan is that every presentable (∞,1)-category comes from a model category, and every adjoint pair between such comes from a Quillen pair of functors ...

2 мар. 2021 г. · I have heard that one application of ∞-categories is that they allow us to formulate a meaningful theory of descent for derived categories.

23 февр. 2010 г. · (∞,1)-categories are equivalent to simplicial categories (categories enriched over simplicial sets). This is outlined in Lurie's higher topoi.

20 янв. 2010 г. · Later in DAGI, Lurie shows that stable infinity categories are automatically enriched in the stable infinity category of spectra. This is ...

4 июл. 2018 г. · We can't define (∞,1)-categories in HoTT in this way since the enrichment must be strict. That is, the composition operation must be strictly associative and ...

1 дек. 2010 г. · There is the notion of monoidal ∞-category, which can be found in Lurie's DAG II. A∞-categories are something like ∞-categories tensored ...

17 авг. 2024 г. · The title of the question says it all. When does the Lurie tensor product of ∞-categories ([Higher Algebra] Section 4.8.1) commute with infinite products?

30 сент. 2014 г. · In fact, for me there is no doubt that (∞,1)−categories are really useful. For example, the work of Lurie/Toën/Vezzosi in Derived Algebraic ...