[Merged by Bors] - feat(category_theory/monoidal/subcategory): full monoidal subcategories #14311
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Co-authored-by: Scott Morrison <scott@tqft.net>
Co-authored-by: Scott Morrison <scott@tqft.net>
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Co-authored-by: Scott Morrison <scott@tqft.net>
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| lemma prop_id [hP : monoidal_predicate P] : P (𝟙_ C) := hP.prop_id' | ||
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| -- For some reason which I don't understand `hP.prop_tensor' hX hY` doesn't work here. | ||
| lemma prop_tensor [hP : monoidal_predicate P] {X Y : C} (hX : P X) (hY : P Y) : P (X ⊗ Y) := | ||
| by { apply hP.prop_tensor', exact hX, exact hY } |
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Alternatively:
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| lemma prop_id [hP : monoidal_predicate P] : P (𝟙_ C) := hP.prop_id' | |
| -- For some reason which I don't understand `hP.prop_tensor' hX hY` doesn't work here. | |
| lemma prop_tensor [hP : monoidal_predicate P] {X Y : C} (hX : P X) (hY : P Y) : P (X ⊗ Y) := | |
| by { apply hP.prop_tensor', exact hX, exact hY } | |
| restate_axiom monoidal_predicate.prop_id' | |
| restate_axiom monoidal_predicate.prop_tensor' | |
| open monoidal_predicate |
(You'll need to remove two explicit P arguments below.)
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| (prop_id' : P (𝟙_ C)) | ||
| (prop_tensor' : ∀ {X Y}, P X → P Y → P (X ⊗ Y)) |
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Not essential, but you could add . obviously here if you like.
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…es (#14311) We use a type synonym for `{X : C // P X}` when `C` is a monoidal category and the property `P` is closed under the monoidal unit and tensor product so that `full_monoidal_subcategory` can be made an instance. Co-authored-by: antoinelab01 <66086247+antoinelab01@users.noreply.github.com>
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…es (#14311) We use a type synonym for `{X : C // P X}` when `C` is a monoidal category and the property `P` is closed under the monoidal unit and tensor product so that `full_monoidal_subcategory` can be made an instance. Co-authored-by: antoinelab01 <66086247+antoinelab01@users.noreply.github.com>
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We use a type synonym for
{X : C // P X}whenCis a monoidal category and the propertyPis closed under the monoidal unit and tensor product so thatfull_monoidal_subcategorycan be made an instance.