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Theorems · Inductive type · category theory

CategoryTheory.Limits.IsIPC

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [CategoryTheory.Limits.HasProducts C] →
      [CategoryTheory.Limits.HasFilteredColimitsOfSize.{w, u_3, v_1, u_1} C] → Prop

A category C has the w-IPC property it satisfies the IPC-property for every ι : Type w.

Defined in
Mathlib.CategoryTheory.Limits.FilteredColimitCommutesProduct
Cited by
1 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasProductsCategoryTheory.Limits.HasFilteredColimitsOfSize
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Around this declaration

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

CategoryTheory.Limits.IsIPC.casesOn · cited by 0IsIPC.casesOnCategoryTheory.Limits.IsIPC.isIPCOfShape · cited by 0IsIPC.isIPCOfShapeCategoryTheory.Limits.IsIPC.recOn · cited by 0IsIPC.recOnCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasProducts · cited by 103Limits.HasProductsCategoryTheory.Limits.HasFilteredColimitsOfSize · cited by 13Limits.HasFilteredColimit…Limits.IsIPCCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

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