Theorems · Theorem · category theory

CategoryTheory.hasTerminal_of_equivalence

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (e : CategoryTheory.Functor D C) [e.IsEquivalence] [CategoryTheory.Limits.HasTerminal C],
  CategoryTheory.Limits.HasTerminal D

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Equivalence
Cited by: 1 results in Mathlib
Foundations: Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.IsEquivalence CategoryTheory.Limits.HasTerminal

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Cites5

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.Functorstatement and proof · cited by 16,252
CategoryTheory.Limits.HasTerminalstatement and proof · cited by 142
CategoryTheory.Functor.IsEquivalencestatement and proof · cited by 111
CategoryTheory.Adjunction.hasLimitsOfShape_of_equivalenceproof · cited by 3

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Equivalence.hasTerminal_iffproof · cited by 4