Relative homological dimensions and Tate cohomology of complexes with respect to cotorsion pairs |
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| Authors: | Xiaoyan Yang Wenjing Chen |
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| Institution: | 1. Department of Mathematics, Northwest Normal University, Lanzhou, Chinayangxy@nwnu.edu.cn;3. Department of Mathematics, Northwest Normal University, Lanzhou, China |
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| Abstract: | Let (𝒳,𝒴) be a complete and hereditary cotorsion pair in a bicomplete abelian category 𝒜. We introduce a Gorenstein category 𝒢(𝒳) and 𝒢(𝒳)-resolution dimension of complexes with respect to (𝒳,𝒴). For complexes with finite 𝒢(𝒳)-resolution dimension, Tate 𝒳-resolutions are constructed. Furthermore, we study relative Tate cohomology of complexes, which is useful for detecting the finiteness of the relative homological dimensions of complexes. |
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| Keywords: | Cotorsion pair Tate resolution |
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