Explicit limits and colimits

This file applies the general API for explicit limits and colimits in CompHausLike P (see the file Mathlib.Topology.Category.CompHausLike.Limits) to the special case of Profinite.

instance Profinite.instHasExplicitPullbacksTotallyDisconnectedSpaceCarrier : CompHausLike.HasExplicitPullbacks fun (Y : TopCat) => TotallyDisconnectedSpace ↑Y

instance Profinite.instHasExplicitFiniteCoproductsTotallyDisconnectedSpaceCarrier : CompHausLike.HasExplicitFiniteCoproducts fun (Y : TopCat) => TotallyDisconnectedSpace ↑Y

@[reducible, inline]

abbrev Profinite.isTerminalPUnit : CategoryTheory.Limits.IsTerminal (of PUnit.{u + 1})

A one-element space is terminal in Profinite

Equations

• Profinite.isTerminalPUnit = CompHausLike.isTerminalPUnit