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Theorems · Definition · category theory

FreeSimplexQuiver

Type

The objects of the free simplex quiver are the natural numbers.

Defined in
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic
Cited by
2 results in Mathlib
Foundations
Depth 1 from the axioms · uses no axioms
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Around this declaration

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

SimplexCategoryGenRel.mk · cited by 39SimplexCategoryGenRel.mkSimplexCategoryGenRel.σ · cited by 26SimplexCategoryGenRel.σSimplexCategoryGenRel.δ · cited by 20SimplexCategoryGenRel.δSimplexCategoryGenRel.toSimplexCategory · cited by 7SimplexCategoryGenRel.toS…FreeSimplexQuiver.homRel · cited by 7FreeSimplexQuiver.homRelFreeSimplexQuiver.mk · cited by 7FreeSimplexQuiver.mkSimplexCategoryGenRel.len · cited by 6SimplexCategoryGenRel.lenFreeSimplexQuiver.Hom · cited by 6FreeSimplexQuiver.HomSimplexCategoryGenRel.multiplicativeClosure_isGenerator_eq_top · cited by 2SimplexCategoryGenRel.mul…FreeSimplexQuiver.Hom.δ.noConfusion · cited by 1δ.noConfusionFreeSimplexQuiver.Hom.σ.noConfusion · cited by 1σ.noConfusionFreeSimplexQuiver.Hom.casesOn · cited by 1Hom.casesOnFreeSimplexQuiver.Hom.recOn · cited by 0Hom.recOnFreeSimplexQuiver.homRel.casesOn · cited by 0homRel.casesOnSimplexCategoryGenRel.exists_P_σ_P_δ_factorization · cited by 0SimplexCategoryGenRel.exi…FreeSimplexQuiverCITED BYCITES

Cites0

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

Nothing in Mathlib beyond the foundations.

Cited by26

Results whose statement or proof uses this declaration.