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Theorems · Definition · algebraic topology

SSet.Truncated.Path

{n : ℕ} → SSet.Truncated (n + 1) → ℕ → Type u

A path of length m in an n + 1-truncated simplicial set X is given by the data of a Path₁ structure on the further 1-truncation of X.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Path
Cited by
37 results in Mathlib
Foundations
Depth 54 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.

SSet.Path · cited by 46SSet.PathSSet.Truncated.spine · cited by 24Truncated.spineSSet.Truncated.Path.arrow · cited by 20Path.arrowSSet.Truncated.Path.vertex · cited by 16Path.vertexSSet.Truncated.StrictSegal.spineToSimplex · cited by 14StrictSegal.spineToSimplexSSet.Truncated.Path.ext' · cited by 6Path.ext'SSet.Truncated.StrictSegal.spineEquiv · cited by 6StrictSegal.spineEquivSSet.Truncated.Path.interval · cited by 5Path.intervalSSet.Truncated.Path.mk₂ · cited by 5Path.mk₂SSet.Truncated.Path.ext · cited by 4Path.extSSet.Truncated.Path.map · cited by 4Path.mapSSet.Truncated.StrictSegal.spineToSimplex_arrow · cited by 3StrictSegal.spineToSimple…SSet.Truncated.StrictSegal.spine_spineToSimplex_apply · cited by 3StrictSegal.spine_spineTo…SSet.Truncated.liftOfStrictSegal.spineEquiv_f₂_arrow_one · cited by 3liftOfStrictSegal.spineEq…SSet.Truncated.liftOfStrictSegal.spineEquiv_f₂_arrow_zero · cited by 3liftOfStrictSegal.spineEq…CategoryTheory.Functor.obj · cited by 19642Functor.objSSet.Truncated · cited by 214SSet.TruncatedSSet.Truncated.Path₁ · cited by 9Truncated.Path₁SSet.Truncated.trunc · cited by 8Truncated.truncTruncated.PathCITED BYCITES

Cites4

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Cited by54

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