Theorems · Theorem · category theory
DirectedSystem.map_map
∀ {ι : Type u_1} {inst : Preorder ι} {F : ι → Type u_4} {f : ⦃i j : ι⦄ → i ≤ j → F i → F j} [self : DirectedSystem F f]
⦃k j i : ι⦄ (hij : i ≤ j) (hjk : j ≤ k) (x : F i), f hjk (f hij x) = f ⋯ x- Defined in
- Mathlib.Order.DirectedInverseSystem
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- DirectedSystem
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- LE.le.transstatement · cited by 3,151
- DirectedSystemstatement and proof · cited by 174
Cited by3
Results whose statement or proof uses this declaration.
- DirectedSystem.map_map'proof · cited by 3
- DirectedSystem.lTensorproof · cited by 1
- DirectedSystem.rTensorproof · cited by 1