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Theorems · Theorem · category theory

SimplexCategory.toCat_obj

∀ (X : SimplexCategory),
  SimplexCategory.toCat.obj X =
    CategoryTheory.Cat.of
      ↑((CategoryTheory.forget₂ PartOrd Preord).obj
          ((CategoryTheory.forget₂ Lat PartOrd).obj
            ((CategoryTheory.forget₂ LinOrd Lat).obj
              ((CategoryTheory.forget₂ NonemptyFinLinOrd LinOrd).obj (NonemptyFinLinOrd.of (Fin (X.len + 1)))))))
Defined in
Mathlib.AlgebraicTopology.SimplexCategory.Basic
Cited by
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Foundations
Depth 59 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.

CategoryTheory.Functor.obj · cited by 19642Functor.objSimplexCategory · cited by 2204SimplexCategoryOrderHom · cited by 934OrderHomCategoryTheory.Cat · cited by 884CategoryTheory.CatSimplexCategory.len · cited by 542SimplexCategory.lenCategoryTheory.forget₂ · cited by 260CategoryTheory.forget₂LatticeHom · cited by 192LatticeHomCategoryTheory.Cat.of · cited by 189Cat.ofPartOrd.carrier · cited by 93PartOrd.carrierPartOrd · cited by 65PartOrdLat.carrier · cited by 58Lat.carrierLinOrd.carrier · cited by 48LinOrd.carrierLinOrd · cited by 46LinOrdLat · cited by 43LatPreord · cited by 42PreordSimplexCategory.toCat_objCITED BYCITES

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