Theorems · Definition · category theory

Condensed.IsDiscrete

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [CategoryTheory.HasWeakSheafify (CategoryTheory.coherentTopology CompHaus) C] → Condensed C → Prop

A condensed object is discrete if it is constant as a sheaf, i.e. isomorphic to a constant sheaf.

Defined in: Mathlib.Condensed.Discrete.Characterization
Cited by: 3 results in Mathlib
Foundations: Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.HasWeakSheafify

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

Cites7

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
TopCatstatement · cited by 1,889
CategoryTheory.HasWeakSheafifystatement and proof · cited by 221
CategoryTheory.coherentTopologystatement and proof · cited by 141
CompHausstatement and proof · cited by 61
Condensedstatement and proof · cited by 20
CategoryTheory.Sheaf.IsConstantproof · cited by 13

Cited by3

Results whose statement or proof uses this declaration.

CondensedMod.isDiscrete_iff_isDiscrete_forgetstatement · cited by 1
CondensedSet.isDiscrete_tfaestatement and proof · cited by 1
CondensedMod.isDiscrete_tfaestatement and proof · cited by 0