Theorems · Inductive type · category theory
DirectedSystem
{ι : Type u_1} → [inst : Preorder ι] → (F : ι → Type u_4) → (⦃i j : ι⦄ → i ≤ j → F i → F j) → PropA directed system is a functor from a category (directed poset) to another category.
- Defined in
- Mathlib.Order.DirectedInverseSystem
- Cited by
- 174 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 5 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement · cited by 7,952
Cited by209
Results whose statement or proof uses this declaration.
- DirectLimitstatement and proof · cited by 103
- DirectLimit.setoidstatement and proof · cited by 65
- DirectLimit.liftstatement and proof · cited by 29
- FirstOrder.Language.DirectLimitstatement and proof · cited by 23
- FirstOrder.Language.DirectLimit.ofstatement and proof · cited by 17
- DirectLimit.inductionstatement and proof · cited by 17
- FirstOrder.Language.DirectLimit.setoidstatement and proof · cited by 14
- DirectLimit.map₀statement and proof · cited by 10
- DirectLimit.eq_of_lestatement and proof · cited by 8
- DirectLimit.map₀_defstatement and proof · cited by 7
- DirectLimit.Module.ofstatement and proof · cited by 7
- DirectLimit.Ring.ofstatement and proof · cited by 7
Showing the 200 most cited of 209.