Theorems · Theorem · category theory
Function.Exact.apply_apply_eq_zero
∀ {M : Type u_2} {N : Type u_4} {P : Type u_6} {f : M → N} {g : N → P} [inst : Zero P],
Function.Exact f g → ∀ (x : M), g (f x) = 0- Defined in
- Mathlib.Algebra.Exact.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- Zero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.mem_range_selfproof · cited by 328
- Function.Exactstatement and proof · cited by 182
Cited by11
Results whose statement or proof uses this declaration.
- AddMonoidHom.injective_of_surjective_of_injective_of_injectiveproof · cited by 3
- AddMonoidHom.exact_iff_of_surjective_of_bijective_of_injectiveproof · cited by 3
- AddMonoidHom.surjective_of_surjective_of_surjective_of_injectiveproof · cited by 3
- Function.Exact.comp_eq_zeroproof · cited by 2
- SnakeLemma.exact_δ_leftproof · cited by 2
- SnakeLemma.exact_δ_rightproof · cited by 2
- Module.Flat.iff_lTensor_preserves_shortComplex_exactproof · cited by 1
- LieAlgebra.Extension.incl_apply_mem_kerproof · cited by 1
- Module.FaithfullyFlat.range_le_ker_of_exact_rTensorproof · cited by 1
- Module.Flat.iff_rTensor_preserves_shortComplex_exactproof · cited by 0
- TopologicalAddGroup.IsSES.inducedMeasure_lt_of_injOnproof · cited by 0