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Theorems · Definition · category theory

ComplexShape.Embedding.BoundaryLE

{ι : Type u_1} → {ι' : Type u_2} → {c : ComplexShape ι} → {c' : ComplexShape ι'} → c.Embedding c' → ι → Prop

The upper boundary of an embedding e : Embedding c c', as a predicate on ι. It is satisfied by j : ι when there exists k' : ι' not in the image of e.f such that c'.Rel (e.f j) k'.

Defined in
Mathlib.Algebra.Homology.Embedding.Boundary
Cited by
19 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

HomologicalComplex.truncLE'XIso · cited by 4HomologicalComplex.truncL…ComplexShape.Embedding.not_boundaryLE_prev · cited by 3Embedding.not_boundaryLE_…HomologicalComplex.truncLE'XIsoCycles · cited by 2HomologicalComplex.truncL…ComplexShape.Embedding.AreComplementary.Boundary.exists₁ · cited by 1Boundary.exists₁ComplexShape.Embedding.AreComplementary.Boundary.indexOfBoundaryLE · cited by 1Boundary.indexOfBoundaryLEComplexShape.Embedding.boundaryLE · cited by 1Embedding.boundaryLEHomologicalComplex.truncLE'Map_f_eq · cited by 0HomologicalComplex.truncL…HomologicalComplex.truncLE'Map_f_eq_cyclesMap · cited by 0HomologicalComplex.truncL…HomologicalComplex.truncLE'_d_eq · cited by 0HomologicalComplex.truncL…HomologicalComplex.truncLE'_d_eq_toCycles · cited by 0HomologicalComplex.truncL…HomologicalComplex.truncLEXIso · cited by 0HomologicalComplex.truncL…HomologicalComplex.truncLEXIsoCycles · cited by 0HomologicalComplex.truncL…ComplexShape.Embedding.AreComplementary.Boundary.equiv · cited by 0Boundary.equivComplexShape.Embedding.AreComplementary.Boundary.fst · cited by 0Boundary.fstComplexShape.Embedding.AreComplementary.Boundary.of_boundaryLE · cited by 0Boundary.of_boundaryLEComplexShape · cited by 1684ComplexShapeComplexShape.Rel · cited by 518ComplexShape.RelComplexShape.Embedding · cited by 337ComplexShape.EmbeddingComplexShape.next · cited by 297ComplexShape.nextComplexShape.Embedding.f · cited by 251Embedding.fEmbedding.BoundaryLECITED BYCITES

Cites5

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

Cited by26

Results whose statement or proof uses this declaration.