Theorems · Theorem · general topology

Topology.IsQuotientMap.lift_comp

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : C(X, Y)} (hf : Topology.IsQuotientMap ⇑f) (g : C(X, Z))
  (h : Function.FactorsThrough ⇑g ⇑f), (hf.lift g h).comp f = g

The obvious triangle induced by IsQuotientMap.lift commutes: `` g X --→ Z | ↗ f | / hf.lift g h v / Y ``

Defined in

Mathlib.Topology.ContinuousMap.Basic

Cited by

2 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace