instFullOppositeOp — Mathlib

English

If F is a full functor F: C → D, then the induced functor F.rightOp: C^{op} ⥤ D is full.

Русский

Если F: C → D полно, то F.rightOp: C^{op} ⥤ D полно.

LaTeX

$$$\\\\forall C [\\\\text{Category}(C)], \\\\forall D [\\\\text{Category}(D)], \\\\forall F: C \\\\to D, \\\\text{Full}(F) \\\\Rightarrow \\\\text{Full}(F^{\\\\mathrm{rightOp}}).$$$

Lean4

instance {F : C ⥤ D} [Full F] : Full F.op where map_surjective f := ⟨(F.preimage f.unop).op, by simp⟩

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