A new model of dg-categories
Abstract
In this article, we develop a new model for the category of dg-categories. Following Rezk's example in the case of classic Segal spaces, we define dg-Segal spaces: functors between free dg-categories of finite type and simplicial spaces to which we add certain properties. We define also complete dg-Segal 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 dg-categories and the homotopy category of functors defined above with a model structure making the complete dg-Segal spaces into its fibrant objects.
Keywords
Cite
@article{arxiv.2308.06417,
title = {A new model of dg-categories},
author = {Elena Dimitriadis Bermejo},
journal= {arXiv preprint arXiv:2308.06417},
year = {2024}
}
Comments
37 pages. Submitted to the Bulletin de la Soci\'et\'e Math\'ematique de France. Replacement due to technical rewrites in chapter 4 due to an inconsistency of construction, and the addition of a lemma before the final proof of the fully-faithfulness