The homotopy category of pseudofunctors and translation cohomology |
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Authors: | Hans-Joachim Baues |
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Affiliation: | a Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany b Universitat de Barcelona, Departament d’Àlgebra i Geometria, Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain |
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Abstract: | We develop the obstruction theory of the 2-category of abelian track categories, pseudofunctors and pseudonatural transformations by using the cohomology of categories. The obstructions are defined in Baues-Wirsching cohomology groups. We introduce translation cohomology to classify endomorphisms in the 2-category of abelian track categories. In a sequel to this paper we will show, under certain conditions which are satisfied by all homotopy categories, that a translation cohomology class determines the exact triangles of a triangulated category. |
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Keywords: | 18D05 18G60 55S35 |
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