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Theorems · Definition · category theory

ComplexShape.embeddingDownNat

(ComplexShape.down ℕ).Embedding (ComplexShape.up ℤ)

The embedding from down ℕ to up ℤ with sends n to -n.

Defined in
Mathlib.Algebra.Homology.Embedding.Basic
Cited by
5 results in Mathlib
Foundations
Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

CategoryTheory.ProjectiveResolution.cochainComplex · cited by 30ProjectiveResolution.coch…CategoryTheory.ProjectiveResolution.cochainComplexXIso · cited by 18ProjectiveResolution.coch…CategoryTheory.ProjectiveResolution.π' · cited by 9ProjectiveResolution.π'CategoryTheory.ProjectiveResolution.cochainComplex_d · cited by 8ProjectiveResolution.coch…CategoryTheory.ProjectiveResolution.Hom.hom' · cited by 5Hom.hom'CategoryTheory.ProjectiveResolution.Hom.hom'_f · cited by 3Hom.hom'_fCategoryTheory.ProjectiveResolution.π'_f_zero · cited by 2ProjectiveResolution.π'_f…ChainComplex.quasiIso_iff_of_projective · cited by 0ChainComplex.quasiIso_iff…ComplexShape.embeddingDownNat_f · cited by 0ComplexShape.embeddingDow…ComplexShape.up · cited by 1123ComplexShape.upComplexShape.down · cited by 605ComplexShape.downComplexShape.Embedding · cited by 337ComplexShape.EmbeddingComplexShape.Embedding.mk' · cited by 1Embedding.mk'ComplexShape.embeddingDownNatCITED BYCITES

Cites4

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

Cited by9

Results whose statement or proof uses this declaration.