Theorems · Theorem · commutative algebra

Module.Relations.Solution.IsPresentation.bijective

∀ {A : Type u} [inst : Ring A] {relations : Module.Relations A} {M : Type v} [inst_1 : AddCommGroup M]
  [inst_2 : Module A M] {solution : relations.Solution M},
  solution.IsPresentation → Function.Bijective ⇑solution.fromQuotient

Defined in: Mathlib.Algebra.Module.Presentation.Basic
Cited by: 6 results in Mathlib
Foundations: Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring AddCommGroup Module

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement · cited by 10,215
Ringstatement and proof · cited by 7,463
Function.Bijectivestatement · cited by 863
Module.Relationsstatement and proof · cited by 97
Module.Relations.Solutionstatement and proof · cited by 70
Module.Relations.Solution.IsPresentationstatement and proof · cited by 39
Module.Relations.Quotientstatement · cited by 22
Module.Relations.Solution.fromQuotientstatement · cited by 12

Cited by7

Results whose statement or proof uses this declaration.

Module.Relations.Solution.isPresentation_iffproof · cited by 3
Module.Relations.Solution.IsPresentation.linearEquivproof · cited by 3
Module.Relations.Solution.IsPresentation.surjective_πproof · cited by 2
Module.Relations.Solution.IsPresentation.postcomp_injectiveproof · cited by 1
Module.Relations.Solution.IsPresentation.ker_πproof · cited by 1
Module.Relations.Solution.IsPresentation.exactproof · cited by 0
Module.Relations.Solution.IsPresentation.of_linearEquivproof · cited by 0