Products, Homotopy Limits and Applications

2009/02/23 by Amit Hogadi, Chenyang Xu, Hogadi, Amit +1 · 1 citation
Computer Science · Mathematics · #14A20 #18E30 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Category Theory (math.CT) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0902.4016

openalex publication_date 2009/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we discuss the derived functors of infinite products and homotopy limits. QC(X), the category of quasi-coherent sheaves on a Deligne-Mumford stack X, usually has the property that the derived functors of product vanish after a finite stage. We use this fact to study the convergence of certain homotopy limits and apply it compare the derived category of QC(X) with certain other closely related triangulated categories.

Cited by

• The dual of Brown representability for some derived categories

Related

• Recognizing quasi-categorical limits and colimits in homotopy coherent\n nerves
• Homotopy limits in the category of dg-categories in terms of A_∞-comodules
• Homotopy (co)limits via homotopy (co)ends in general combinatorial model categories
• Completeness results for quasi-categories of algebras, homotopy limits, and related general constructions
• Homotopy limits of complexes