Theorems · Theorem · global analysis

StructureGroupoid.compatible

∀ {H : Type u_5} [inst : TopologicalSpace H] (G : StructureGroupoid H) {M : Type u_6} [inst_1 : TopologicalSpace M]
  [inst_2 : ChartedSpace H M] [HasGroupoid M G] {e e' : OpenPartialHomeomorph M H},
  e ∈ atlas H M → e' ∈ atlas H M → e.symm.trans e' ∈ G

Reformulate in the StructureGroupoid namespace the compatibility condition of charts in a charted space admitting a structure groupoid, to make it more easily accessible with dot notation.

Defined in

Mathlib.Geometry.Manifold.HasGroupoid

Cited by

3 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceChartedSpaceHasGroupoid