Theorems · Definition · algebraic topology
SSet.stdSimplex.triangle
{n : ℕ} → (a b c : Fin (n + 1)) → a ≤ b → b ≤ c → (SSet.stdSimplex.obj { len := n }).obj (Opposite.op { len := 2 })The triangle in the standard simplex with vertices a, b, and c.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement · cited by 1,283
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- SSet.stdSimplexstatement · cited by 499
- SSet.stdSimplex.objMkproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- SSet.horn.primitiveTriangleproof · cited by 3
- SSet.horn.primitiveTriangle_coestatement · cited by 0
- SSet.stdSimplex.coe_triangle_down_toOrderHomstatement · cited by 0
- SSet.stdSimplex.triangle.congr_simpstatement and proof · cited by 0