Adjoint functors and triangulated categories

M Grime

Adjoint functors and triangulated categories

M Grime

School of Mathematics

Research output: Non-textual form › Web publication/site

Abstract

We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a tripe of functors. This includes the cases of homotopy and stable module categories. These categories naturally fit into a framework of relative derived categories, and once we prove that there are decent resolutions of complexes, we are able to prove many familiar results in homological algebra.

Translated title of the contribution	Adjoint functors and triangulated categories
Original language	English
Publisher	Cornell University Press
Publication status	Published - 20 Aug 2007

Bibliographical note

Other: To appear in Communications in Algebra

Access to Document

http://arxiv.org/abs/math/0601575

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abstract = "We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a tripe of functors. This includes the cases of homotopy and stable module categories. These categories naturally fit into a framework of relative derived categories, and once we prove that there are decent resolutions of complexes, we are able to prove many familiar results in homological algebra.",

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