A new model for dgcategories
Abstract
In this document, we develop a new model for the category of dgcategories. Following Rezk's example in the case of classic Segal spaces, we define dgSegal spaces: functors between free dgcategories of finite type and simplicial spaces to which we add certain properties. We define also complete dgSegal spaces, and make their relationship to classic Segal spaces explicit. With the help of two new hypercover constructions, and up to a certain hypothesis, we prove that there exists an equivalence between the homotopy category of dgcategories and the homotopy category of functors defined above with a model structure making the complete dgSegal spaces into its fibrant objects.
 Publication:

arXiv eprints
 Pub Date:
 February 2023
 DOI:
 10.48550/arXiv.2302.00430
 arXiv:
 arXiv:2302.00430
 Bibcode:
 2023arXiv230200430D
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  KTheory and Homology
 EPrint:
 PhD manuscript, supervised by Bertrand To\"en and Fr\'ed\'eric D\'eglise