Theorems · Definition · algebraic geometry

AlgebraicGeometry.PresheafedSpace.colimitCoconeIsColimit

{J : Type u'} →
  [inst : CategoryTheory.Category.{v', u'} J] →
    {C : Type u} →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        [inst_2 : CategoryTheory.Limits.HasColimitsOfShape J TopCat] →
          [inst_3 : ∀ (X : TopCat), CategoryTheory.Limits.HasLimitsOfShape Jᵒᵖ (TopCat.Presheaf C X)] →
            [CategoryTheory.Limits.HasLimitsOfShape Jᵒᵖ C] →
              (F : CategoryTheory.Functor J (AlgebraicGeometry.PresheafedSpace C)) →
                CategoryTheory.Limits.IsColimit (AlgebraicGeometry.PresheafedSpace.colimitCocone F)

Auxiliary definition for AlgebraicGeometry.PresheafedSpace.instHasColimits.

Defined in

Mathlib.Geometry.RingedSpace.PresheafedSpace.HasColimits

Cited by

1 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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