2023/02/01 by Elena Dimitriadis Bermejo, Bermejo, Elena Dimitriadis
Mathematics · Medicine · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2302.00430
openalex publication_date 2023/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this document, 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.