iso — Mathlib

English

There is a canonical isomorphism between the functor LocallyConstant on Condensed sets and the discrete functor, i.e., LocallyConstant.functor is isomorphic to discrete(Type).

Русский

Существует каноническое изоморфизм между LocallyConstant на Condensed-наборы и дискретным функтором, то есть LocallyConstant.functor изоморфен дискретному типу.

LaTeX

$$LocallyConstant.functor ≅ discrete (Type (u+1))$$

Lean4

/-- `CondensedSet.LocallyConstant.functor` is isomorphic to `Condensed.discrete`
(by uniqueness of adjoints).
-/
noncomputable def iso : functor ≅ discrete (Type (u + 1)) :=
  (LocallyConstant.adjunction _ _).leftAdjointUniq (discreteUnderlyingAdj _)

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