[Merged by Bors] - feat(CategoryTheory/Triangulated/Adjunction): the left adjoint of a triangulated functor is triangulated#20543
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[Merged by Bors] - feat(CategoryTheory/Triangulated/Adjunction): the left adjoint of a triangulated functor is triangulated#20543
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Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
…r-community/mathlib4 into SM.adjointTriangulated
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…riangulated functor is triangulated (#20543) If a functor `G : D ⥤ C` between pretriangulated categories is triangulated, and if we have an adjunction `F ⊣ G` (that commutes with the shifts), then `F` is also a triangulated functor. We prove this from the symmetric statement (`F` triangulated implies `G` triangulated) using opposite categories. - [ ] depends on: #20363 Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com>
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If a functor
G : D ⥤ Cbetween pretriangulated categories is triangulated, and if we have an adjunctionF ⊣ G(that commutes with the shifts), thenFis also a triangulated functor.We prove this from the symmetric statement (
Ftriangulated impliesGtriangulated) using opposite categories.CommShiftstructures on adjunctions are compatible with opposites and pullbacks #20363