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The lower extension groups and quotient categories
- Source :
- Comptes Rendus Mathematique. 357:832-840
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
Abstract
- 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.<br />Comment: 10 pages
- Subjects :
- 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
Subjects
Details
- ISSN :
- 1631073X
- Volume :
- 357
- Database :
- OpenAIRE
- Journal :
- Comptes Rendus Mathematique
- Accession number :
- edsair.doi.dedup.....9f1930a2618c1e801f06c0a56c9a013f