A Grothendieck opfibration approach to constructions of Waldhausen category
- A+
：Zhenxing Di (Huaqiao University)
： 2024-10-25 15:45
：Conference Room C503 at Administration Building at Haiyun Campus
Speaker：Zhenxing Di (Huaqiao University)
Time：2024-10-25, 15:45
Location：Conference Room C503 at Administration Building at Haiyun Campus
Abstract:
Given a Grothendieck opfibration p: T→B, we describe a method to construct a Waldhausen category structure on the total category T via combining Waldhausen category structures on the fibers TA for A∈Ob(B) and the basis category B. As an application, we show that if E is a Waldhausen category with small coproducts such that the class of cofibrations is the left part of a weak factorization system in E, then the representation category Rep(Q, coE) of a left rooted quiver Q is a Waldhausen category, where coE is the subcategory of E whose morphisms are cofibrations.
