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Purity and Almost Split Morphisms in Abstract Homotopy Categories: A Unified Approach via Brown Representability

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Abstract

Our aim in this paper is to develop a theory of purity and to prove in a unified conceptual way the existence of almost split morphisms, almost split sequences and almost split triangles in abstract homotopy categories, a rather omnipresent class of categories of interest in representation theory. Our main tool for doing this is the classical Brown representability theorem.

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  1. Department of Mathematics, University of the Aegean, 83200, Karlovassi, Samos, Greece. e-mail

    Apostolos Beligiannis

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  1. Apostolos Beligiannis
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Beligiannis, A. Purity and Almost Split Morphisms in Abstract Homotopy Categories: A Unified Approach via Brown Representability. Algebras and Representation Theory 5, 483–525 (2002). https://doi.org/10.1023/A:1020535022658

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