English
There is a sheaf of types on M giving to each open set U the type of functions U→M' satisfying LiftProp P.
Русский
Существует она ть локальная п Predicates: живая сфера типов на M, сопоставляющая каждому открытом множество U тип функций U→M', удовлетворяющих LiftProp P.
LaTeX
$$StructureGroupoid.LocalInvariantProp.sheaf hG$$
Lean4
/-- Let `P` be a `LocalInvariantProp` for functions between spaces with the groupoids `G`, `G'`
and let `M`, `M'` be charted spaces modelled on the model spaces of those groupoids. Then there is
a sheaf of types on `M` which, to each open set `U` in `M`, associates the type of bundled
functions from `U` to `M'` satisfying the lift of `P`. -/
def sheaf (hG : LocalInvariantProp G G' P) : TopCat.Sheaf (Type u) (TopCat.of M) :=
TopCat.subsheafToTypes (hG.localPredicate M M')
