Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.ShortComplex.ShortExact.epi_g

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {S : CategoryTheory.ShortComplex C}, S.ShortExact → CategoryTheory.Epi S.g
Defined in
Mathlib.Algebra.Homology.ShortComplex.ShortExact
Cited by
17 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

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

CategoryTheory.ShortComplex.ShortExact.map_of_exact · cited by 23ShortExact.map_of_exactCategoryTheory.ShortComplex.ShortExact.homology_exact₂ · cited by 6ShortExact.homology_exact₂CategoryTheory.Functor.exact_tfae · cited by 3Functor.exact_tfaeHomologicalComplex.HomologySequence.epi_homologyMap_τ₃ · cited by 1HomologySequence.epi_homo…CategoryTheory.ObjectProperty.prop_X₃_of_shortExact · cited by 1ObjectProperty.prop_X₃_of…CategoryTheory.ShortComplex.ShortExact.ab_surjective_g · cited by 1ShortExact.ab_surjective_gHomologicalComplex.HomologySequence.mono_homologyMap_τ₃ · cited by 1HomologySequence.mono_hom…CategoryTheory.ShortComplex.ShortExact.surjective_g · cited by 1ShortExact.surjective_gTopCat.Sheaf.IsFlasque.epi_of_shortExact · cited by 1IsFlasque.epi_of_shortExa…CategoryTheory.ShortComplex.ShortExact.exactAt_X₃ · cited by 1ShortExact.exactAt_X₃CategoryTheory.ShortComplex.isIso₂_of_shortExact_of_isIso₁₃ · cited by 1ShortComplex.isIso₂_of_sh…CategoryTheory.JointlyReflectIsomorphisms.shortExact_iff · cited by 0JointlyReflectIsomorphism…Rep.shortExact_res · cited by 0Rep.shortExact_resHomologicalComplex.shortExact_iff_degreewise_shortExact · cited by 0HomologicalComplex.shortE…ModuleCat.linearIndependent_shortExact · cited by 0ModuleCat.linearIndepende…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.X₂ · cited by 1115ShortComplex.X₂CategoryTheory.ShortComplex.X₃ · cited by 876ShortComplex.X₃CategoryTheory.Epi · cited by 688CategoryTheory.EpiCategoryTheory.ShortComplex.g · cited by 658ShortComplex.gCategoryTheory.ShortComplex.ShortExact · cited by 232ShortComplex.ShortExactShortExact.epi_gCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by17

Results whose statement or proof uses this declaration.