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Theorems · Definition · category theory

CategoryTheory.ShortComplex.f

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → (self : CategoryTheory.ShortComplex C) → self.X₁ ⟶ self.X₂

the first morphism of a ShortComplex

Defined in
Mathlib.Algebra.Homology.ShortComplex.Basic
Cited by
653 results in Mathlib
Foundations
Depth 4 from the axioms, rests on 11 definitions · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.ShortComplex.map · cited by 188ShortComplex.mapCategoryTheory.ShortComplex.op · cited by 88ShortComplex.opCategoryTheory.ShortComplex.zero · cited by 76ShortComplex.zeroCategoryTheory.ShortComplex.LeftHomologyData.f' · cited by 61LeftHomologyData.f'CategoryTheory.ShortComplex.unop · cited by 44ShortComplex.unopCategoryTheory.ShortComplex.ShortExact.extClass · cited by 36ShortExact.extClassCategoryTheory.ShortComplex.isoMk · cited by 30ShortComplex.isoMkCategoryTheory.ShortComplex.ShortExact.singleTriangle · cited by 26ShortExact.singleTriangleCategoryTheory.ShortComplex.exact_of_g_is_cokernel · cited by 25ShortComplex.exact_of_g_i…CategoryTheory.ShortComplex.LeftHomologyData.map · cited by 25LeftHomologyData.mapCategoryTheory.ShortComplex.RightHomologyData.map · cited by 23RightHomologyData.mapCategoryTheory.ShortComplex.ShortExact.map_of_exact · cited by 23ShortExact.map_of_exactCategoryTheory.ShortComplex.exact_of_f_is_kernel · cited by 22ShortComplex.exact_of_f_i…CategoryTheory.ShortComplex.LeftHomologyData.f'_i · cited by 21LeftHomologyData.f'_iCategoryTheory.ShortComplex.moduleCatToCycles · cited by 20ShortComplex.moduleCatToC…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.X₂ · cited by 1115ShortComplex.X₂CategoryTheory.ShortComplex.X₁ · cited by 889ShortComplex.X₁ShortComplex.fCITED BYCITES

Cites6

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Cited by820

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