File: Mathlib/CategoryTheory/Limits/Preserves/Opposites.lean

full_name: CategoryTheory.Limits.preservesLimitOp
code: /-- If `F : C ⥤ D` preserves colimits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves
    limits of `K : J ⥤ Cᵒᵖ`. -/
def preservesLimitOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ D) [PreservesColimit K.leftOp F] :
    PreservesLimit K F.op 
goal: CategoryTheory.Limits.PreservesLimit K F.op

full_name: CategoryTheory.Limits.preservesLimitLeftOp
code: /-- If `F : C ⥤ Dᵒᵖ` preserves colimits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.left_op : Cᵒᵖ ⥤ D`
    preserves limits of `K : J ⥤ Cᵒᵖ`. -/
def preservesLimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesColimit K.leftOp F] :
    PreservesLimit K F.leftOp 
goal: CategoryTheory.Limits.PreservesLimit K F.leftOp

full_name: CategoryTheory.Limits.preservesLimitRightOp
code: /-- If `F : Cᵒᵖ ⥤ D` preserves colimits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.right_op : C ⥤ Dᵒᵖ` preserves
    limits of `K : J ⥤ C`. -/
def preservesLimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesColimit K.op F] :
    PreservesLimit K F.rightOp 
goal: CategoryTheory.Limits.PreservesLimit K F.rightOp

full_name: CategoryTheory.Limits.preservesLimitUnop
code: /-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.unop : C ⥤ D` preserves
    limits of `K : J ⥤ C`. -/
def preservesLimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimit K.op F] :
    PreservesLimit K F.unop 
goal: CategoryTheory.Limits.PreservesLimit K F.unop

full_name: CategoryTheory.Limits.preservesColimitOp
code: /-- If `F : C ⥤ D` preserves limits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves
    colimits of `K : J ⥤ Cᵒᵖ`. -/
def preservesColimitOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ D) [PreservesLimit K.leftOp F] :
    PreservesColimit K F.op 
goal: CategoryTheory.Limits.PreservesColimit K F.op

full_name: CategoryTheory.Limits.preservesColimitLeftOp
code: /-- If `F : C ⥤ Dᵒᵖ` preserves limits of `K.left_op : Jᵒᵖ ⥤ C`, then `F.left_op : Cᵒᵖ ⥤ D` preserves
    colimits of `K : J ⥤ Cᵒᵖ`. -/
def preservesColimitLeftOp (K : J ⥤ Cᵒᵖ) (F : C ⥤ Dᵒᵖ) [PreservesLimit K.leftOp F] :
    PreservesColimit K F.leftOp 
goal: CategoryTheory.Limits.PreservesColimit K F.leftOp

full_name: CategoryTheory.Limits.preservesColimitRightOp
code: /-- If `F : Cᵒᵖ ⥤ D` preserves limits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.right_op : C ⥤ Dᵒᵖ` preserves
    colimits of `K : J ⥤ C`. -/
def preservesColimitRightOp (K : J ⥤ C) (F : Cᵒᵖ ⥤ D) [PreservesLimit K.op F] :
    PreservesColimit K F.rightOp 
goal: CategoryTheory.Limits.PreservesColimit K F.rightOp

full_name: CategoryTheory.Limits.preservesColimitUnop
code: /-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits of `K.op : Jᵒᵖ ⥤ Cᵒᵖ`, then `F.unop : C ⥤ D` preserves
    colimits of `K : J ⥤ C`. -/
def preservesColimitUnop (K : J ⥤ C) (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimit K.op F] :
    PreservesColimit K F.unop 
goal: CategoryTheory.Limits.PreservesColimit K F.unop

full_name: CategoryTheory.Limits.preservesLimitsOfShapeOp
code: /-- If `F : C ⥤ D` preserves colimits of shape `Jᵒᵖ`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits of
    shape `J`. -/
def preservesLimitsOfShapeOp (F : C ⥤ D) [PreservesColimitsOfShape Jᵒᵖ F] :
    PreservesLimitsOfShape J F.op 
goal: CategoryTheory.Limits.PreservesLimitsOfShape J F.op

full_name: CategoryTheory.Limits.preservesLimitsOfShapeLeftOp
code: /-- If `F : C ⥤ Dᵒᵖ` preserves colimits of shape `Jᵒᵖ`, then `F.left_op : Cᵒᵖ ⥤ D` preserves limits
    of shape `J`. -/
def preservesLimitsOfShapeLeftOp (F : C ⥤ Dᵒᵖ) [PreservesColimitsOfShape Jᵒᵖ F] :
    PreservesLimitsOfShape J F.leftOp 
goal: CategoryTheory.Limits.PreservesLimitsOfShape J F.leftOp

full_name: CategoryTheory.Limits.preservesLimitsOfShapeRightOp
code: /-- If `F : Cᵒᵖ ⥤ D` preserves colimits of shape `Jᵒᵖ`, then `F.right_op : C ⥤ Dᵒᵖ` preserves limits
    of shape `J`. -/
def preservesLimitsOfShapeRightOp (F : Cᵒᵖ ⥤ D) [PreservesColimitsOfShape Jᵒᵖ F] :
    PreservesLimitsOfShape J F.rightOp 
goal: CategoryTheory.Limits.PreservesLimitsOfShape J F.rightOp

full_name: CategoryTheory.Limits.preservesLimitsOfShapeUnop
code: /-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits of shape `Jᵒᵖ`, then `F.unop : C ⥤ D` preserves limits of
    shape `J`. -/
def preservesLimitsOfShapeUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimitsOfShape Jᵒᵖ F] :
    PreservesLimitsOfShape J F.unop 
goal: CategoryTheory.Limits.PreservesLimitsOfShape J F.unop

full_name: CategoryTheory.Limits.preservesColimitsOfShapeOp
code: /-- If `F : C ⥤ D` preserves limits of shape `Jᵒᵖ`, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits of
    shape `J`. -/
def preservesColimitsOfShapeOp (F : C ⥤ D) [PreservesLimitsOfShape Jᵒᵖ F] :
    PreservesColimitsOfShape J F.op 
goal: CategoryTheory.Limits.PreservesColimitsOfShape J F.op

full_name: CategoryTheory.Limits.preservesColimitsOfShapeLeftOp
code: /-- If `F : C ⥤ Dᵒᵖ` preserves limits of shape `Jᵒᵖ`, then `F.left_op : Cᵒᵖ ⥤ D` preserves colimits
    of shape `J`. -/
def preservesColimitsOfShapeLeftOp (F : C ⥤ Dᵒᵖ) [PreservesLimitsOfShape Jᵒᵖ F] :
    PreservesColimitsOfShape J F.leftOp 
goal: CategoryTheory.Limits.PreservesColimitsOfShape J F.leftOp

full_name: CategoryTheory.Limits.preservesColimitsOfShapeRightOp
code: /-- If `F : Cᵒᵖ ⥤ D` preserves limits of shape `Jᵒᵖ`, then `F.right_op : C ⥤ Dᵒᵖ` preserves colimits
    of shape `J`. -/
def preservesColimitsOfShapeRightOp (F : Cᵒᵖ ⥤ D) [PreservesLimitsOfShape Jᵒᵖ F] :
    PreservesColimitsOfShape J F.rightOp 
goal: CategoryTheory.Limits.PreservesColimitsOfShape J F.rightOp

full_name: CategoryTheory.Limits.preservesColimitsOfShapeUnop
code: /-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits of shape `Jᵒᵖ`, then `F.unop : C ⥤ D` preserves colimits
    of shape `J`. -/
def preservesColimitsOfShapeUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimitsOfShape Jᵒᵖ F] :
    PreservesColimitsOfShape J F.unop 
goal: CategoryTheory.Limits.PreservesColimitsOfShape J F.unop

full_name: CategoryTheory.Limits.preservesLimitsOp
code: /-- If `F : C ⥤ D` preserves colimits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits. -/
def preservesLimitsOp (F : C ⥤ D) [PreservesColimits F] : PreservesLimits F.op 
goal: CategoryTheory.Limits.PreservesLimits F.op

full_name: CategoryTheory.Limits.preservesLimitsLeftOp
code: /-- If `F : C ⥤ Dᵒᵖ` preserves colimits, then `F.left_op : Cᵒᵖ ⥤ D` preserves limits. -/
def preservesLimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesColimits F] : PreservesLimits F.leftOp 
goal: CategoryTheory.Limits.PreservesLimits F.leftOp

full_name: CategoryTheory.Limits.preservesLimitsRightOp
code: /-- If `F : Cᵒᵖ ⥤ D` preserves colimits, then `F.right_op : C ⥤ Dᵒᵖ` preserves limits. -/
def preservesLimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesColimits F] : PreservesLimits F.rightOp 
goal: CategoryTheory.Limits.PreservesLimits F.rightOp

full_name: CategoryTheory.Limits.preservesLimitsUnop
code: /-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits, then `F.unop : C ⥤ D` preserves limits. -/
def preservesLimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesColimits F] : PreservesLimits F.unop 
goal: CategoryTheory.Limits.PreservesLimits F.unop

full_name: CategoryTheory.Limits.perservesColimitsOp
code: /-- If `F : C ⥤ D` preserves limits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves colimits. -/
def perservesColimitsOp (F : C ⥤ D) [PreservesLimits F] : PreservesColimits F.op 
goal: CategoryTheory.Limits.PreservesColimits F.op

full_name: CategoryTheory.Limits.preservesColimitsLeftOp
code: /-- If `F : C ⥤ Dᵒᵖ` preserves limits, then `F.left_op : Cᵒᵖ ⥤ D` preserves colimits. -/
def preservesColimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesLimits F] : PreservesColimits F.leftOp 
goal: CategoryTheory.Limits.PreservesColimits F.leftOp

full_name: CategoryTheory.Limits.preservesColimitsRightOp
code: /-- If `F : Cᵒᵖ ⥤ D` preserves limits, then `F.right_op : C ⥤ Dᵒᵖ` preserves colimits. -/
def preservesColimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesLimits F] : PreservesColimits F.rightOp 
goal: CategoryTheory.Limits.PreservesColimits F.rightOp

full_name: CategoryTheory.Limits.preservesColimitsUnop
code: /-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves limits, then `F.unop : C ⥤ D` preserves colimits. -/
def preservesColimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesLimits F] : PreservesColimits F.unop 
goal: CategoryTheory.Limits.PreservesColimits F.unop

full_name: CategoryTheory.Limits.preservesFiniteLimitsOp
code: /-- If `F : C ⥤ D` preserves finite colimits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite
    limits. -/
def preservesFiniteLimitsOp (F : C ⥤ D) [PreservesFiniteColimits F] :
    PreservesFiniteLimits F.op 
goal: CategoryTheory.Limits.PreservesFiniteLimits F.op

full_name: CategoryTheory.Limits.preservesFiniteLimitsLeftOp
code: /-- If `F : C ⥤ Dᵒᵖ` preserves finite colimits, then `F.left_op : Cᵒᵖ ⥤ D` preserves finite
    limits. -/
def preservesFiniteLimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesFiniteColimits F] :
    PreservesFiniteLimits F.leftOp 
goal: CategoryTheory.Limits.PreservesFiniteLimits F.leftOp

full_name: CategoryTheory.Limits.preservesFiniteLimitsRightOp
code: /-- If `F : Cᵒᵖ ⥤ D` preserves finite colimits, then `F.right_op : C ⥤ Dᵒᵖ` preserves finite
    limits. -/
def preservesFiniteLimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesFiniteColimits F] :
    PreservesFiniteLimits F.rightOp 
goal: CategoryTheory.Limits.PreservesFiniteLimits F.rightOp

full_name: CategoryTheory.Limits.preservesFiniteLimitsUnop
code: /-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite colimits, then `F.unop : C ⥤ D` preserves finite
    limits. -/
def preservesFiniteLimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesFiniteColimits F] :
    PreservesFiniteLimits F.unop 
goal: CategoryTheory.Limits.PreservesFiniteLimits F.unop

full_name: CategoryTheory.Limits.preservesFiniteColimitsOp
code: /-- If `F : C ⥤ D` preserves finite limits, then `F.op : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite
    colimits. -/
def preservesFiniteColimitsOp (F : C ⥤ D) [PreservesFiniteLimits F] :
    PreservesFiniteColimits F.op 
goal: CategoryTheory.Limits.PreservesFiniteColimits F.op

full_name: CategoryTheory.Limits.preservesFiniteColimitsLeftOp
code: /-- If `F : C ⥤ Dᵒᵖ` preserves finite limits, then `F.left_op : Cᵒᵖ ⥤ D` preserves finite
    colimits. -/
def preservesFiniteColimitsLeftOp (F : C ⥤ Dᵒᵖ) [PreservesFiniteLimits F] :
    PreservesFiniteColimits F.leftOp 
goal: CategoryTheory.Limits.PreservesFiniteColimits F.leftOp

full_name: CategoryTheory.Limits.preservesFiniteColimitsRightOp
code: /-- If `F : Cᵒᵖ ⥤ D` preserves finite limits, then `F.right_op : C ⥤ Dᵒᵖ` preserves finite
    colimits. -/
def preservesFiniteColimitsRightOp (F : Cᵒᵖ ⥤ D) [PreservesFiniteLimits F] :
    PreservesFiniteColimits F.rightOp 
goal: CategoryTheory.Limits.PreservesFiniteColimits F.rightOp

full_name: CategoryTheory.Limits.preservesFiniteColimitsUnop
code: /-- If `F : Cᵒᵖ ⥤ Dᵒᵖ` preserves finite limits, then `F.unop : C ⥤ D` preserves finite
    colimits. -/
def preservesFiniteColimitsUnop (F : Cᵒᵖ ⥤ Dᵒᵖ) [PreservesFiniteLimits F] :
    PreservesFiniteColimits F.unop 
goal: CategoryTheory.Limits.PreservesFiniteColimits F.unop