Theorems · Definition · category theory
Function.Exact
{M : Type u_2} → {N : Type u_4} → {P : Type u_6} → (M → N) → (N → P) → [Zero P] → PropThe maps f and g form an exact pair:
g y = 0 iff y belongs to the image of f.
- Defined in
- Mathlib.Algebra.Exact.Basic
- Cited by
- 182 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 18 definitions · uses no axioms
- Assumes
- Zero
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 by204
Results whose statement or proof uses this declaration.
- LinearMap.exact_iffstatement · cited by 27
- Function.Exact.linearMap_ker_eqstatement and proof · cited by 18
- LinearMap.exact_subtype_ker_mapstatement · cited by 11
- lTensor_exactstatement and proof · cited by 11
- Function.Exact.apply_apply_eq_zerostatement and proof · cited by 11
- CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exactstatement and proof · cited by 11
- LinearMap.exact_subtype_mkQstatement · cited by 10
- rTensor_exactstatement and proof · cited by 9
- Function.Exact.linearMap_comp_eq_zerostatement and proof · cited by 9
- CategoryTheory.ShortComplex.ab_exact_iff_function_exactstatement and proof · cited by 8
- Module.Flat.lTensor_exactstatement and proof · cited by 7
- Module.length_eq_add_of_exactstatement and proof · cited by 6
Showing the 200 most cited of 204.