2015-04-25 04:20:59 +00:00
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/-
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Copyright (c) 2015 Jakob von Raumer. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Floris van Doorn, Jakob von Raumer
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-/
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2015-10-23 05:12:34 +00:00
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import .functor.basic
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2015-04-25 04:20:59 +00:00
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open is_trunc eq
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namespace category
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structure strict_precategory [class] (ob : Type) extends precategory ob :=
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mk' :: (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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2015-10-02 23:54:27 +00:00
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-- TODO: move to constructions.cat?
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definition precategory_strict_precategory [constructor] : precategory Strict_precategory :=
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precategory.mk (λ A B, A ⇒ B)
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(λ A B C G F, G ∘f F)
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(λ A, 1)
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(λ A B C D, functor.assoc)
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(λ A B, functor.id_left)
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(λ A B, functor.id_right)
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2015-04-25 04:20:59 +00:00
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2015-10-02 23:54:27 +00:00
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definition Precategory_strict_precategory [constructor] := precategory.Mk precategory_strict_precategory
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2015-04-25 04:20:59 +00:00
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namespace ops
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2015-10-02 23:54:27 +00:00
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abbreviation Cat := Precategory_strict_precategory
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2015-04-25 04:20:59 +00:00
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end ops
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end category
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