Theorems · Definition · category theory

CategoryTheory.Arrow.shrinkEquiv

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : Small.{w, u} C] → CategoryTheory.Arrow (Shrink.{w, u} C) ≃ CategoryTheory.Arrow C

The bijection Arrow (Shrink C) ≃ Arrow C.

Defined in: Mathlib.CategoryTheory.Comma.CardinalArrow
Cited by: 1 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category Small

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Cites10

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
CategoryTheory.Functor.objproof · cited by 19,642
Equivstatement · cited by 8,337
CategoryTheory.Equivalence.functorproof · cited by 1,268
CategoryTheory.Equivalence.inverseproof · cited by 1,130
CategoryTheory.Arrowstatement · cited by 713
Smallstatement and proof · cited by 369
Shrinkstatement · cited by 132
CategoryTheory.Functor.mapArrowproof · cited by 31
CategoryTheory.Shrink.equivalenceproof · cited by 18

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.hasCardinalLT_arrow_shrink_iffproof · cited by 0