The Yoneda isomorphism commutes with homology

Abstract

We show that, for a right exact functor from an abelian category to abelian groups, Yoneda's isomorphism commutes with homology and, hence, with functor derivation. Then we extend this result to semiabelian domains. An interpretation in terms of satellites and higher central extensions follows. As an application, we develop semiabelian (higher) torsion theories and the associated theory of (higher) universal (central) extensions.

arXiv commentFixed an inaccuracy in (3.6)

References in corpus (11)

• Higher Hopf formulae for homology via Galois Theory
• On the second cohomology group in semi-abelian categories
• Higher central extensions and Hopf formulae
• Protoadditive functors, derived torsion theories and homology
• Universal central extensions in semi-abelian categories
• Resolutions, higher extensions and the relative Mal'tsev axiom
• On satellites in semi-abelian categories: Homology without projectives
• Higher central extensions and cohomology
• Simplicial homotopy in semi-abelian categories
• Peri-abelian categories and the universal central extension condition
• On satellites in arbitrary categories

Cited by in corpus (8)

• Higher central extensions and cohomology
• Auslander's formula and correspondence for exact categories
• Localizations of (one-sided) exact categories
• Triangular Matrix Categories I: Dualizing Varieties and generalized one-point extension
• Groupoids and skeletal categories form a pretorsion theory in $\mathsf{Cat}$
• Non-additive derived functors via chain resolutions
• Higher extensions in exact Mal'tsev categories: distributivity of congruences and the $3^n$-Lemma
• Projective crossed modules in semi-abelian categories