Theorems · Definition · category theory
Function.MulExact
{M : Type u_2} → {N : Type u_4} → {P : Type u_6} → (M → N) → (N → P) → [One P] → PropThe maps f and g form an exact pair: g y = 1 iff y belongs to the image of f.
- Defined in
- Mathlib.Algebra.Exact.Basic
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- One
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangeproof · cited by 4,705
Cited by30
Results whose statement or proof uses this declaration.
- Function.MulExact.apply_apply_eq_onestatement and proof · cited by 5
- MonoidHom.injective_of_surjective_of_injective_of_injectivestatement and proof · cited by 2
- MonoidHom.surjective_of_surjective_of_surjective_of_injectivestatement and proof · cited by 2
- MonoidHom.mulExact_iffstatement · cited by 2
- Function.MulExact.iff_of_ladder_mulEquivstatement · cited by 2
- Function.MulExact.iff_rangeFactorizationstatement · cited by 2
- TopologicalGroup.IsSES.mulExactstatement · cited by 2
- MonoidHom.injective_of_surjective_of_injective_of_right_exactstatement and proof · cited by 1
- MonoidHom.surjective_of_surjective_of_injective_of_left_exactstatement and proof · cited by 1
- MonoidHom.mulExact_iff_of_surjective_of_bijective_of_injectivestatement and proof · cited by 1
- MonoidHom.mulExact_of_comp_eq_one_of_ker_le_rangestatement · cited by 1
- Function.MulExact.comp_eq_onestatement and proof · cited by 1