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doc(Manifold/Charted): document the fields of Pregroupoid (#11930)
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grunweg committed Apr 18, 2024
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7 changes: 7 additions & 0 deletions Mathlib/Geometry/Manifold/ChartedSpace.lean
Expand Up @@ -342,12 +342,19 @@ both the function and its inverse have some property. If this property is stable
one gets a groupoid. `Pregroupoid` bundles the properties needed for this construction, with the
groupoid of smooth functions with smooth inverses as an application. -/
structure Pregroupoid (H : Type*) [TopologicalSpace H] where
/-- Property describing membership in this groupoid: the pregroupoid "contains"
all functions `H → H` having the pregroupoid property on some `s : Set H` -/
property : (H → H) → Set H → Prop
/-- The pregroupoid property is stable under composition -/
comp : ∀ {f g u v}, property f u → property g v →
IsOpen u → IsOpen v → IsOpen (u ∩ f ⁻¹' v) → property (g ∘ f) (u ∩ f ⁻¹' v)
/-- Pregroupoids contain the identity map (on `univ`) -/
id_mem : property id univ
/-- The pregroupoid property is "local", in the sense that `f` has the pregroupoid property on `u`
iff its restriction to each open subset of `u` has it -/
locality :
∀ {f u}, IsOpen u → (∀ x ∈ u, ∃ v, IsOpen v ∧ x ∈ v ∧ property f (u ∩ v)) → property f u
/-- If `f = g` on `u` and `property f u`, then `property g u` -/
congr : ∀ {f g : H → H} {u}, IsOpen u → (∀ x ∈ u, g x = f x) → property f u → property g u
#align pregroupoid Pregroupoid

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1 change: 0 additions & 1 deletion scripts/nolints.json
Expand Up @@ -337,7 +337,6 @@
["docBlame", "PowerBasis.basis"],
["docBlame", "PowerBasis.dim"],
["docBlame", "PowerBasis.gen"],
["docBlame", "Pregroupoid.property"],
["docBlame", "PresheafOfModules.presheaf"],
["docBlame", "Pretrivialization.baseSet"],
["docBlame", "PrimeSpectrum.asIdeal"],
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