Theorems · Definition · algebraic geometry

AlgebraicGeometry.PresheafedSpace.colimit

{J : Type u'} →
  [inst : CategoryTheory.Category.{v', u'} J] →
    {C : Type u} →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        [CategoryTheory.Limits.HasColimitsOfShape J TopCat] →
          [∀ (X : TopCat), CategoryTheory.Limits.HasLimitsOfShape Jᵒᵖ (TopCat.Presheaf C X)] →
            CategoryTheory.Functor J (AlgebraicGeometry.PresheafedSpace C) → AlgebraicGeometry.PresheafedSpace C

Auxiliary definition for AlgebraicGeometry.PresheafedSpace.instHasColimits.

Defined in

Mathlib.Geometry.RingedSpace.PresheafedSpace.HasColimits

Cited by

6 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasLimitsOfShape