Theorems · Inductive type · category theory
CategoryTheory.ShortComplex.ShortExact
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → CategoryTheory.ShortComplex C → PropA short complex S is short exact if it is exact, S.f is a mono and S.g is an epi.
- Cited by
- 232 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 by267
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.ShortExact.extClassstatement and proof · cited by 36
- HomologicalComplex.HomologySequence.snakeInputstatement and proof · cited by 27
- CategoryTheory.ShortComplex.ShortExact.singleTrianglestatement and proof · cited by 26
- CategoryTheory.ShortComplex.ShortExact.map_of_exactstatement and proof · cited by 23
- CategoryTheory.ShortComplex.ShortExact.δstatement and proof · cited by 22
- CategoryTheory.ShortComplex.ShortExact.exactstatement and proof · cited by 20
- CategoryTheory.ShortComplex.ShortExact.mono_fstatement and proof · cited by 19
- DerivedCategory.triangleOfSESstatement and proof · cited by 17
- CategoryTheory.ShortComplex.ShortExact.epi_gstatement and proof · cited by 17
- CategoryTheory.ShortComplex.ShortExact.singleδstatement and proof · cited by 12
- groupCohomology.map_cochainsFunctor_shortExactstatement and proof · cited by 9
- groupHomology.map_chainsFunctor_shortExactstatement and proof · cited by 8
Showing the 200 most cited of 267.