Derived categories of functors and quiver sheaves

Author(s)

Gneri, P. O. ; Jardim, M. ; Silva, D. D.

• Document type: Journal article
• Source: JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. 21, n. 07, p. 26-pg., 2022-07-01.

Abstract

Let C be small category and A an arbitrary category. Consider the category C(A) whose objects are functors from C to A and whose morphisms are natural transformations. Let B be another category, and again, consider the category C(B). Now, given a functor F : A -> B we construct the induced functor F-C : C(A) -> C(B). Assuming A and B to be abelian categories, it follows that the categories C(A) and C(B) are also abelian. We have two main goals: first, to find a relationship between the derived category D(C(A)) and the category C(D(A)); second relate the functors R(F-C) and (RF)(C) : C(D(A)) -> C(D(B)). We apply the general results obtained to the special case of quiver sheaves. (AU)

• FAPESP's process: 18/21391-1 - Gauge theory and algebraic geometry
• Grantee: Marcos Benevenuto Jardim
• Support Opportunities: Research Projects - Thematic Grants