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Theorems · Definition · category theory

CategoryTheory.ShortComplex.pOpcycles

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (S : CategoryTheory.ShortComplex C) → [inst_2 : S.HasRightHomology] → S.X₂ ⟶ S.opcycles

The projection S.X₂ ⟶ S.opcycles.

Defined in
Mathlib.Algebra.Homology.ShortComplex.RightHomology
Cited by
84 results in Mathlib
Foundations
Depth 7 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasRightHomology
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Around this declaration

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

HomologicalComplex.pOpcycles · cited by 71HomologicalComplex.pOpcyc…CategoryTheory.ShortComplex.exact_of_g_is_cokernel · cited by 25ShortComplex.exact_of_g_i…CategoryTheory.ShortComplex.p_descOpcycles · cited by 9ShortComplex.p_descOpcycl…CategoryTheory.ShortComplex.exact_iff_mono · cited by 8ShortComplex.exact_iff_mo…CategoryTheory.ShortComplex.p_fromOpcycles · cited by 8ShortComplex.p_fromOpcycl…CategoryTheory.ShortComplex.Exact.epi_f · cited by 8Exact.epi_fCategoryTheory.ShortComplex.RightHomologyData.canonical · cited by 7RightHomologyData.canonic…CategoryTheory.ShortComplex.opcyclesIsoX₂ · cited by 6ShortComplex.opcyclesIsoX₂CategoryTheory.ShortComplex.p_opcyclesMap · cited by 6ShortComplex.p_opcyclesMapCategoryTheory.ShortComplex.Exact.comp_descToInjective · cited by 6Exact.comp_descToInjectiveCategoryTheory.ShortComplex.RightHomologyData.p_comp_opcyclesIso_inv · cited by 5RightHomologyData.p_comp_…CategoryTheory.ShortComplex.opcyclesIsCokernel · cited by 5ShortComplex.opcyclesIsCo…CategoryTheory.ShortComplex.f_pOpcycles · cited by 5ShortComplex.f_pOpcyclesCategoryTheory.ShortComplex.RightHomologyData.pOpcycles_comp_opcyclesIso_hom · cited by 4RightHomologyData.pOpcycl…CategoryTheory.ShortComplex.homology_π_ι · cited by 4ShortComplex.homology_π_ιCategoryTheory.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.opcycles · cited by 192ShortComplex.opcyclesCategoryTheory.ShortComplex.HasRightHomology · cited by 125ShortComplex.HasRightHomo…CategoryTheory.ShortComplex.RightHomologyData.p · cited by 84RightHomologyData.pCategoryTheory.ShortComplex.rightHomologyData · cited by 64ShortComplex.rightHomolog…ShortComplex.pOpcyclesCITED BYCITES

Cites9

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Cited by94

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