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Theorems · Inductive type · category theory

CategoryTheory.Limits.ReflectsFiniteColimits

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor C D → Prop

A functor is said to reflect finite colimits, if it reflects all colimits of shape J, where J : Type is a finite category.

Defined in
Mathlib.CategoryTheory.Limits.Preserves.Finite
Cited by
19 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.HasExactLimitsOfShape.domain_of_functor · cited by 1HasExactLimitsOfShape.dom…CategoryTheory.Limits.ReflectsFiniteColimits.casesOn · cited by 0ReflectsFiniteColimits.ca…CategoryTheory.Limits.ReflectsFiniteColimits.recOn · cited by 0ReflectsFiniteColimits.re…CategoryTheory.Limits.reflectsFiniteColimits_leftOp · cited by 0Limits.reflectsFiniteColi…CategoryTheory.Limits.reflectsFiniteColimits_of_leftOp · cited by 0Limits.reflectsFiniteColi…CategoryTheory.Limits.reflectsFiniteColimits_of_op · cited by 0Limits.reflectsFiniteColi…CategoryTheory.Limits.reflectsFiniteColimits_of_rightOp · cited by 0Limits.reflectsFiniteColi…CategoryTheory.Limits.reflectsFiniteColimits_of_unop · cited by 0Limits.reflectsFiniteColi…CategoryTheory.Limits.reflectsFiniteColimits_op · cited by 0Limits.reflectsFiniteColi…CategoryTheory.Limits.reflectsFiniteColimits_rightOp · cited by 0Limits.reflectsFiniteColi…CategoryTheory.Limits.reflectsFiniteColimits_unop · cited by 0Limits.reflectsFiniteColi…CategoryTheory.Limits.reflectsFiniteLimits_leftOp · cited by 0Limits.reflectsFiniteLimi…CategoryTheory.Limits.reflectsFiniteLimits_of_leftOp · cited by 0Limits.reflectsFiniteLimi…CategoryTheory.Limits.reflectsFiniteLimits_of_op · cited by 0Limits.reflectsFiniteLimi…CategoryTheory.Limits.preservesFiniteColimits_of_reflects_of_preserves · cited by 0Limits.preservesFiniteCol…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorLimits.ReflectsFiniteColimitsCITED BYCITES

Cites2

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Cited by21

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