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fix namespace
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javra committed Dec 11, 2024
1 parent aab916e commit 90da537
Showing 1 changed file with 14 additions and 3 deletions.
17 changes: 14 additions & 3 deletions Mathlib/CategoryTheory/Limits/IsConnected.lean
Original file line number Diff line number Diff line change
Expand Up @@ -39,7 +39,9 @@ unit-valued, singleton, colimit

universe w v u

namespace CategoryTheory.Limits.Types
namespace CategoryTheory

namespace Limits.Types

variable (C : Type u) [Category.{v} C]

Expand Down Expand Up @@ -111,8 +113,15 @@ theorem isConnected_iff_isColimit_pUnitCocone :
simp only [isConnected_iff_colimit_constPUnitFunctor_iso_pUnit.{w} C]
exact ⟨colimit.isoColimitCocone colimitCocone⟩

end Limits.Types

namespace Functor

open Limits.Types

universe v₂ u₂
variable {C : Type u} {D : Type u₂} [Category.{v} C] [Category.{v₂} D]

variable {C : Type u} [Category.{v} C] {D : Type u₂} [Category.{v₂} D]

/-- The domain of a final functor is connected if and only if its codomain is connected. -/
theorem isConnected_iff_of_final (F : C ⥤ D) [F.Final] : IsConnected C ↔ IsConnected D := by
Expand All @@ -126,4 +135,6 @@ theorem isConnected_iff_of_initial (F : C ⥤ D) [F.Initial] : IsConnected C ↔
rw [isConnected_iff_isConnected_op C, isConnected_iff_isConnected_op D]
exact isConnected_iff_of_final F.op

end CategoryTheory.Limits.Types
end Functor

end CategoryTheory

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