Theorems · Theorem · algebraic topology

SSet.S.mk_map_eq_iff_of_mono

∀ {X : SSet} {n m : ℕ} (x : X.obj (Opposite.op { len := n })) (f : { len := m } ⟶ { len := n }) [CategoryTheory.Mono f],
  { dim := m, simplex := (CategoryTheory.ConcreteCategory.hom (X.map f.op)) x } = { dim := n, simplex := x } ↔
    CategoryTheory.IsIso f

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.Simplices

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Mono