Homotopic morphisms are defined for E-triangles in extriangulated categories so that any morphism of E-triangles decomposes into or can be adjusted to homotopic morphisms, yielding 4x4 lemma variants and a characterization of weakly idempotent complete extriangulated categories.
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Homotopic morphisms and diagram theorems in extriangulated categories
Homotopic morphisms are defined for E-triangles in extriangulated categories so that any morphism of E-triangles decomposes into or can be adjusted to homotopic morphisms, yielding 4x4 lemma variants and a characterization of weakly idempotent complete extriangulated categories.