[Merged by Bors] - feat(CategoryTheory/Triangulated): homological functors #11759
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A functor `F : C ⥤ A` from a pretriangulated category to an abelian category is homological iff it sends distinguished triangles in `C` to exact sequences in `A`. In this PR, we define the corresponding type class `F.IsHomological`. If `F` is a homological functor, we introduce the strictly full triangulated subcategory `F.homologicalKernel`.
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A functor `F : C ⥤ A` from a pretriangulated category to an abelian category is homological iff it sends distinguished triangles in `C` to exact sequences in `A`. In this PR, we define the corresponding type class `F.IsHomological`. If `F` is a homological functor, we introduce the strictly full triangulated subcategory `F.homologicalKernel`.
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A functor `F : C ⥤ A` from a pretriangulated category to an abelian category is homological iff it sends distinguished triangles in `C` to exact sequences in `A`. In this PR, we define the corresponding type class `F.IsHomological`. If `F` is a homological functor, we introduce the strictly full triangulated subcategory `F.homologicalKernel`.
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A functor
F : C ⥤ Afrom a pretriangulated category to an abelian category is homological iff it sends distinguished triangles inCto exact sequences inA. In this PR, we define the corresponding type classF.IsHomological. IfFis a homological functor, we introduce the strictly full triangulated subcategoryF.homologicalKernel.