46 lines
1.3 KiB
Text
46 lines
1.3 KiB
Text
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import .basic .functor
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open category is_trunc eq function sigma sigma.ops
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namespace category
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structure strict_precategory[class] (ob : Type) extends precategory ob :=
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(is_hset_ob : is_hset ob)
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attribute strict_precategory.is_hset_ob [instance]
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definition strict_precategory.mk' [reducible] (ob : Type) (C : precategory ob)
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(H : is_hset ob) : strict_precategory ob :=
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precategory.rec_on C strict_precategory.mk H
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structure Strict_precategory : Type :=
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(carrier : Type)
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(struct : strict_precategory carrier)
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attribute Strict_precategory.struct [instance] [coercion]
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definition Strict_precategory.to_Precategory [coercion] [reducible]
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(C : Strict_precategory) : Precategory :=
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Precategory.mk (Strict_precategory.carrier C) C
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open functor
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definition precat_strict_precat : precategory Strict_precategory :=
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precategory.mk (λ a b, functor a b)
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(λ a b, @functor.is_hset_functor a b _)
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(λ a b c g f, functor.compose g f)
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(λ a, functor.id)
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(λ a b c d h g f, !functor.assoc)
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(λ a b f, !functor.id_left)
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(λ a b f, !functor.id_right)
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definition Precat_of_strict_precats := precategory.Mk precat_strict_precat
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namespace ops
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abbreviation SPreCat := Precat_of_strict_precats
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--attribute precat_strict_precat [instance]
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end ops
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end category
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