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On Auslander's formula and cohereditary torsion pairs

Banerjee, Abhishek (2018) On Auslander's formula and cohereditary torsion pairs. In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 20 (6).

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Official URL: http://dx.doi.org/10.1142/S0219199717500717

Abstract

For a small abelian category C, Auslander's formula allows us to express C as a quotient of the category mod - C of coherent functors on C. We consider an abelian category with the added structure of a cohereditary torsion pair tau = (T, F). We prove versions of Auslander's formula for the torsion-free class F of C, for the derived torsion-free, class D-b(F) of the triangulated category D-b(C) as well as the induced torsion-free class in the ind-category Ind - C of C. Further, for a given regular cardinal alpha, we also consider the category mod(alpha) - C of alpha-presentable objects in the functor category Fun(C-OP, Ab). Then, under certain conditions, we show that the torsion-free class can be recovered as a subquotient of mod(alpha) - C.

Item Type: Journal Article
Additional Information: Copy right for this article belong to WORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE
Keywords: Auslander's formula; coherent functors; cohereditary torsion pairs
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 11 Sep 2018 14:56
Last Modified: 11 Sep 2018 14:56
URI: http://eprints.iisc.ac.in/id/eprint/60647

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