Exact couples in semiabelian categories revisited

Yaroslav Kopylov, Sven Ake Wegner

Research output: Contribution to journalArticle

Abstract

Consider an exact couple in a semiabelian category in the sense of Palamodov, i.e., in an additive category in which every morphism has a kernel as well as a cokernel and the induced morphism between coimage and image is always monic and epic. Assume that the morphisms in the couple are strict, i.e., they induce even isomorphisms between their corresponding coimages and images. We show that the classical construction of Eckmann and Hilton in this case produces two derived couples which are connected by a natural bimorphism. The two couples correspond to the a priori distinct cohomology objects, the left resp. right cohomology, associated with the initial exact couple. The derivation process can be iterated under additional assumptions.

Original languageEnglish
Pages (from-to)264-270
Number of pages7
JournalJournal of Algebra
Volume414
DOIs
Publication statusPublished - Sep 15 2014
Externally publishedYes

Fingerprint

Semi-abelian Category
Morphism
Cohomology
Monic
Morphisms
Isomorphism
kernel
Distinct

Keywords

  • Exact couple
  • Quasiabelian category
  • Semiabelian category
  • Spectral sequence

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Exact couples in semiabelian categories revisited. / Kopylov, Yaroslav; Wegner, Sven Ake.

In: Journal of Algebra, Vol. 414, 15.09.2014, p. 264-270.

Research output: Contribution to journalArticle

Kopylov, Yaroslav ; Wegner, Sven Ake. / Exact couples in semiabelian categories revisited. In: Journal of Algebra. 2014 ; Vol. 414. pp. 264-270.
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