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Theorems · Definition · category theory

TopCat.isInitialPEmpty

CategoryTheory.Limits.IsInitial (TopCat.of PEmpty.{u + 1})

The initial object of Top is PEmpty.

Defined in
Mathlib.Topology.Category.TopCat.Limits.Basic
Cited by
2 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

TopPair.ofTopCat · cited by 8TopPair.ofTopCatTopPair.inclAdjProj₁ · cited by 2TopPair.inclAdjProj₁TopCat.initialIsoPEmpty · cited by 0TopCat.initialIsoPEmptyTopPair.j · cited by 0TopPair.jTopCat.IsInducing.empty · cited by 0IsInducing.emptyTopPair.inclAdjProj₁_counit_app · cited by 0TopPair.inclAdjProj₁_coun…TopCat · cited by 1889TopCatCategoryTheory.Limits.IsInitial · cited by 158Limits.IsInitialCategoryTheory.Limits.IsInitial.ofUnique · cited by 0IsInitial.ofUniqueTopCat.isInitialPEmptyCITED BYCITES

Cites3

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Cited by6

Results whose statement or proof uses this declaration.