locallyOfFinitePresentation_comp — Mathlib

English

If f and g are locally of finite presentation, then f ≫ g is locally of finite presentation.

Русский

Если f и g локально конечны презентационно, то f ∘ g локально конечного типа.

LaTeX

$$$\text{LocallyOfFinitePresentation}(f) \land \text{LocallyOfFinitePresentation}(g) \Rightarrow \text{LocallyOfFinitePresentation}(f \circ g).$$$

Lean4

instance locallyOfFinitePresentation_comp {X Y Z : Scheme.{u}} (f : X ⟶ Y) (g : Y ⟶ Z)
    [hf : LocallyOfFinitePresentation f] [hg : LocallyOfFinitePresentation g] : LocallyOfFinitePresentation (f ≫ g) :=
  MorphismProperty.comp_mem _ f g hf hg

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