Commit 2024-06-24 10:09 85a75afa
View on Github →feat: the mapping cone of a monomorphism, up to a quasi-isomorphism (#13675)
In this PR, given a short exact sequence S
in the category of cochain complexes in an abelian category, we compare the homology sequence of S
, and the homology sequence of the homological functor on the homotopy category applied to the distinguished triangle of the mapping cone of the monomorphism S.f
. In particular, up to a quasi-isomorphism, the mapping cone of S.f
identifies to S.X₃
.
In future PRs, this shall be used in order to attach a distinguished triangle in the derived category to S
(#13742), and compare the homology sequence of S
and the homology sequence attached to this distinguished triangle.