mk — Mathlib · SciLib

English

A morphism in SimplexCategory from a to b is given by a monotone order-preserving map Fin(a.len+1) → Fin(b.len+1).

Русский

Морфизм из a в b в SimplexCategory задаётся монотонной биекцией Fin(a.len+1) → Fin(b.len+1).

LaTeX

$$$\\mathrm{Hom}(a,b) = \\{ f:\\mathrm{Fin}(a.len+1) \\to\\mathrm{Fin}(b.len+1) \\mid f \\text{ is order-preserving} \\}$$$

Lean4

/-- Make a morphism in `SimplexCategory` from a monotone map of `Fin`'s. -/
def mk {a b : SimplexCategory} (f : Fin (a.len + 1) →o Fin (b.len + 1)) : SimplexCategory.Hom a b :=
  f

Похожие утверждения