For a rigid object M, the presentation functor P from pr(M) to 2-term complexes over End(M) is full, dense, detects extriangles, and induces a mutation-commuting bijection between basic relative cluster-tilting objects and basic 2-term silting objects.
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From objects finitely presented by a rigid object in a triangulated category to 2-term complexes
For a rigid object M, the presentation functor P from pr(M) to 2-term complexes over End(M) is full, dense, detects extriangles, and induces a mutation-commuting bijection between basic relative cluster-tilting objects and basic 2-term silting objects.