Theorems · Theorem · category theory
CategoryTheory.zigzag_isPreconnected
∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J],
(∀ (j₁ j₂ : J), CategoryTheory.Zigzag j₁ j₂) → CategoryTheory.IsPreconnected J- Defined in
- Mathlib.CategoryTheory.IsConnected
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- Relation.ReflTransGenproof · cited by 104
- CategoryTheory.IsPreconnectedstatement · cited by 25
- CategoryTheory.Zigzagstatement and proof · cited by 23
- CategoryTheory.Zagproof · cited by 19
- CategoryTheory.IsPreconnected.of_constant_of_preserves_morphismsproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.zigzag_isConnectedproof · cited by 8
- CategoryTheory.isPreconnected_of_zigzagproof · cited by 1
- CategoryTheory.IsCofilteredOrEmpty.isPreconnectedproof · cited by 1
- CategoryTheory.IsFilteredOrEmpty.isPreconnectedproof · cited by 1