Theorems · Inductive type · category theory
CategoryTheory.ShortComplex.Exact
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → CategoryTheory.ShortComplex C → PropThe assertion that the short complex S : ShortComplex C is exact.
- Cited by
- 292 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 4 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Limits.HasZeroMorphismsstatement · cited by 3,275
- CategoryTheory.ShortComplexstatement · cited by 1,850
Cited by320
Results whose statement or proof uses this declaration.
- HomologicalComplex.ExactAtproof · cited by 44
- CategoryTheory.ShortComplex.exact_of_g_is_cokernelstatement · cited by 25
- CategoryTheory.ShortComplex.exact_of_f_is_kernelstatement · cited by 22
- CategoryTheory.ComposableArrows.Exact.exactstatement · cited by 22
- CategoryTheory.ShortComplex.Exact.exact_toComposableArrowsstatement and proof · cited by 20
- CategoryTheory.ShortComplex.ShortExact.exactstatement · cited by 20
- CategoryTheory.ShortComplex.exact_of_isostatement and proof · cited by 18
- CategoryTheory.ShortComplex.Exact.exact_up_to_refinementsstatement and proof · cited by 14
- CategoryTheory.ShortComplex.exact_iff_exact_up_to_refinementsstatement · cited by 14
- CategoryTheory.ShortComplex.Exact.fIsKernelstatement and proof · cited by 12
- CategoryTheory.ShortComplex.Exact.hasHomologystatement and proof · cited by 12
- CategoryTheory.ShortComplex.Exact.gIsCokernelstatement and proof · cited by 11
Showing the 200 most cited of 320.