(also nonabelian homological algebra)
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For $F : \mathcal{A} \to \mathcal{B}$ a left exact additive functor between abelian categories, an object $A \in \mathcal{A}$ is $F$-acyclic if the right derived functor of $F$ has no cohomology on $A$ in positive degree
A resolution by $F$-acyclic objects serves to compute the derived functor of $F$. See at derived functor in homological algebra β Via acyclic resolutions
See most references on homological algebra.
Also:
Michael Barr, Acyclic models, Canadian J. Math. 48 2 (1996) 258β273 [doi:10.4153/CJM-1996-013-x, pdf, pdf]
Michael Barr, Acyclic models, CRM Monograph Series 17 (2002) [ams:crmm-17, pdf, pdf]
Last revised on November 4, 2023 at 07:16:08. See the history of this page for a list of all contributions to it.