The lower extension groups and quotient categories
| Autor: | Xiao-Wu Chen, Xiaofa Chen |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Additive category
Pure mathematics Quotient category Homotopy category 010102 general mathematics Zero (complex analysis) General Medicine Mathematics::Algebraic Topology 01 natural sciences Cohomology Mathematics::K-Theory and Homology Mathematics::Category Theory Bounded function 0103 physical sciences FOS: Mathematics Homological algebra 010307 mathematical physics Representation Theory (math.RT) 0101 mathematics Mathematics - Representation Theory Quotient Mathematics |
| Zdroj: | Comptes Rendus Mathematique. 357:832-840 |
| ISSN: | 1631-073X |
| Popis: | For a certain full additive subcategory X of an additive category A, one defines the lower extension groups in relative homological algebra. We show that these groups are isomorphic to the suspended Hom groups in the Verdier quotient category of the bounded homotopy category of A by that of X. Alternatively, these groups are isomorphic to the negative cohomological groups of the Hom complexes in the dg quotient category A/X, where both A and X are viewed as dg categories concentrated in degree zero. Comment: 10 pages |
| Databáze: | OpenAIRE |
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