Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.nonempty_iSup
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {α : Sort u_1} (P : α → CategoryTheory.ObjectProperty C)
(a : α) [(P a).Nonempty], (⨆ a, P a).Nonempty- Cited by
- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- iSupstatement · cited by 2,415
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.ObjectProperty.Nonemptystatement and proof · cited by 13
- CategoryTheory.ObjectProperty.nonempty_of_propproof · cited by 5
- CategoryTheory.ObjectProperty.prop_iSup_iffproof · cited by 3
- CategoryTheory.ObjectProperty.arbitraryproof · cited by 3
- CategoryTheory.ObjectProperty.prop_arbitraryproof · cited by 2
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