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arXiv · 1705.04930

The homotopy category of flat functors

Esmaeil Hosseini·Ali Zaghian
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Abstract

Let C be a small category and G be a tensor Grothendieck category. We define a notion of atness in the category Fun(C; G) of all covariant functors from C to G and show that the inclusion K(FlatA) ---> K(A) has a right adjoint where K(A) is the homotopy category of A and K(FlatA) its subcategory consisting of complexes of at functors. In addition, we find a replacement for the quotient Dpac(FlatA) = K(FlatA)Kp(FlatA) of triangulated categories where Kp(FlatA) is the homotopy category of all pure acyclic complexes of at functors.

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Esmaeil Hosseini, Ali Zaghian. 2017-11-16. The homotopy category of flat functors. https://arxiv.org/abs/1705.04930

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