Mathlib Map

Theorems · Definition · order theory

Function.pullbackDiagonal

{X : Type u_1} → {Y : Sort u_2} → (f : X → Y) → Set (Function.Pullback f f)

The diagonal $\Delta(X) \subseteq X \times_Y X$.

Defined in
Mathlib.Data.Set.Prod
Cited by
6 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

isSeparatedMap_iff_isClosed_diagonal · cited by 4isSeparatedMap_iff_isClos…isLocallyInjective_iff_isOpen_diagonal · cited by 3isLocallyInjective_iff_is…Function.Injective.preimage_pullbackDiagonal · cited by 2Injective.preimage_pullba…range_toPullbackDiag · cited by 2range_toPullbackDiagimage_toPullbackDiag · cited by 1image_toPullbackDiagpreimage_map_fst_pullbackDiagonal · cited by 1preimage_map_fst_pullback…Set · cited by 53352SetSet.ofPred · cited by 6101Set.ofPredFunction.Pullback · cited by 29Function.PullbackFunction.Pullback.snd · cited by 4Pullback.sndFunction.Pullback.fst · cited by 2Pullback.fstFunction.pullbackDiagonalCITED BYCITES

Cites5

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

Cited by6

Results whose statement or proof uses this declaration.