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Mathlib.AlgebraicTopology.SimplicialSet.Boundary

The boundary of the standard simplex #

We introduce the boundary ∂Δ[n] of the standard simplex Δ[n]. (These notations become available by doing open Simplicial.)

Future work #

There isn't yet a complete API for simplices, boundaries, and horns. As an example, we should have a function that constructs from a non-surjective order-preserving function Fin n → Fin n a morphism Δ[n] ⟶ ∂Δ[n].

The boundary ∂Δ[n] of the n-th standard simplex consists of all m-simplices of stdSimplex n that are not surjective (when viewed as monotone function m → n).

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      The boundary ∂Δ[n] of the n-th standard simplex

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