Theorems · Theorem · logic and foundations
small_of_surjective
∀ {α : Type v} {β : Type w} [Small.{u, v} α] {f : α → β}, Function.Surjective f → Small.{u, w} β- Defined in
- Mathlib.Logic.Small.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Small
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.
- Smallstatement and proof · cited by 369
- small_of_injectiveproof · cited by 15
- Function.injective_surjInvproof · cited by 14
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.EssentiallySmall.exists_small_leproof · cited by 7
- OrzechProperty.injective_of_surjective_of_injectiveproof · cited by 5
- Algebra.ZariskisMainProperty.of_finiteType_of_weaklyQuasiFiniteAtproof · cited by 3
- ModuleCat.hasInjectiveDimensionLE_iff_forall_maximalSpectrumproof · cited by 2
- small_of_injective_of_existsproof · cited by 2
- ModuleCat.hasProjectiveDimensionLE_iff_forall_maximalSpectrumproof · cited by 2
- ModuleCat.localizedModule_hasInjectiveDimensionLEproof · cited by 2
- ModuleCat.localizedModule_hasProjectiveDimensionLEproof · cited by 2
- CategoryTheory.FinallySmall.exists_of_isFilteredproof · cited by 1
- CategoryTheory.hasExt_of_enoughInjectivesproof · cited by 0
- CategoryTheory.hasExt_of_enoughProjectivesproof · cited by 0