Rigidification of Quasi-categories

نویسندگان

  • DANIEL DUGGER
  • DAVID I. SPIVAK
چکیده

We give a new construction for rigidifying a quasi-category into a simplicial category, and prove that it is weakly equivalent to the rigidification given by Lurie. Our construction comes from the use of necklaces, which are simplicial sets obtained by stringing simplices together. As an application of these methods, we use our model to reprove some basic facts from [L] about the rigidification process.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Mapping Spaces in Quasi-categories

We apply the Dwyer-Kan theory of homotopy function complexes in model categories to the study of mapping spaces in quasi-categories. Using this, together with our work on rigidification from [DS1], we give a streamlined proof of the Quillen equivalence between quasi-categories and simplicial categories. Some useful material about relative mapping spaces in quasi-categories is developed along th...

متن کامل

Gene-engineered rigidification of membrane lipids enhances the cold inducibility of gene expression in synechocystis.

A sudden decrease in ambient temperature induces the expression of a number of genes in poikilothermic organisms. We report here that the cold inducibility of gene expression in Synechocystis sp. PCC 6803 was enhanced by the rigidification of membrane lipids that was engineered by disruption of genes for fatty acid desaturases. DNA microarray analysis revealed that cold-inducible genes could be...

متن کامل

Categories isomorphic to the category of $L$-fuzzy closure system spaces

In this paper, new definitions of $L$-fuzzy closure operator, $L$-fuzzy interior operator, $L$-fuzzy remote neighborhood system, $L$-fuzzy neighborhood system and $L$-fuzzy quasi-coincident neighborhood system are proposed. It is proved that the category of $L$-fuzzy closure spaces, the category of $L$-fuzzy interior spaces, the category of $L$-fuzzy remote neighborhood spaces, the category of ...

متن کامل

On the structure of simplicial categories associated to quasi - categories

The homotopy coherent nerve from simplicial categories to simplicial sets and its left adjoint C are important to the study of (∞, 1)-categories because they provide a means for comparing two models of their respective homotopy theories, giving a Quillen equivalence between the model structures for quasi-categories and simplicial categories. The functor C also gives a cofibrant replacement for ...

متن کامل

Completeness Results for Quasi-categories of Algebras, Homotopy Limits, and Related General Constructions

Consider a diagram of quasi-categories that admit and functors that preserve limits or colimits of a fixed shape. We show that any weighted limit whose weight is a projective cofibrant simplicial functor is again a quasi-category admitting these (co)limits and that they are preserved by the functors in the limit cone. In particular, the BousfieldKan homotopy limit of a diagram of quasi-categori...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009