# Adjunctions regarding the category of topological spaces #

This file shows that the forgetful functor from topological spaces to types has a left and right adjoint, given by Top.discrete, resp. Top.trivial, the functors which equip a type with the discrete, resp. trivial, topology.

Equipping a type with the discrete topology is left adjoint to the forgetful functor Top ⥤ Type.

Equations
@[simp]
@[simp]
Top.adj₁.counit = {app := λ (X : Top), {to_fun := id (Top.discrete.obj X), continuous_to_fun := _}, naturality' := Top.adj₁._proof_3}
@[simp]
Equipping a type with the trivial topology is right adjoint to the forgetful functor Top ⥤ Type.