Theorems · Theorem · category theory

SimplexCategory.Truncated.Hom.tr_comp

∀ {n : ℕ} {a b c : SimplexCategory} (f : a ⟶ b) (g : b ⟶ c)
  (ha : autoParam (a.len ≤ n) SimplexCategory.Truncated.Hom.tr_comp._auto_1)
  (hb : autoParam (b.len ≤ n) SimplexCategory.Truncated.Hom.tr_comp._auto_3)
  (hc : autoParam (c.len ≤ n) SimplexCategory.Truncated.Hom.tr_comp._auto_5),
  SimplexCategory.Truncated.Hom.tr (CategoryTheory.CategoryStruct.comp f g) ha hc =
    CategoryTheory.CategoryStruct.comp (SimplexCategory.Truncated.Hom.tr f ha hb)
      (SimplexCategory.Truncated.Hom.tr g hb hc)

Defined in: Mathlib.AlgebraicTopology.SimplexCategory.Defs
Cited by: 8 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Quot.sound

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Cites6

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
SimplexCategorystatement and proof · cited by 2,204
CategoryTheory.ObjectProperty.FullSubcategorystatement · cited by 726
SimplexCategory.lenstatement and proof · cited by 542
SimplexCategory.Truncated.Hom.trstatement · cited by 43

Cited by8

Results whose statement or proof uses this declaration.

SSet.Truncated.spine_map_subintervalproof · cited by 2
SSet.Truncated.StrictSegal.spineToSimplex_edgeproof · cited by 1
SimplexCategory.Truncated.Hom.tr_comp_assocproof · cited by 0
SSet.Truncated.StrictSegal.spine_δ_arrow_eqproof · cited by 0
SSet.Truncated.StrictSegal.spine_δ_arrow_gtproof · cited by 0
SSet.Truncated.StrictSegal.spine_δ_arrow_ltproof · cited by 0
SSet.Truncated.StrictSegal.spine_δ_vertex_geproof · cited by 0
SSet.Truncated.StrictSegal.spine_δ_vertex_ltproof · cited by 0