2014-10-09 05:57:41 +00:00
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-- Copyright (c) 2014 Floris van Doorn. All rights reserved.
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-- Released under Apache 2.0 license as described in the file LICENSE.
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-- Author: Floris van Doorn
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2014-11-04 00:22:30 +00:00
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import .constructions
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2014-10-09 05:57:41 +00:00
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open eq eq.ops category functor natural_transformation category.ops prod category.product
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namespace adjoint
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--representable functor
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2014-11-04 00:22:30 +00:00
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definition foo (C : Category) : C ×c C ⇒ C ×c C := functor.id
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2014-10-09 05:57:41 +00:00
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2014-11-04 00:22:30 +00:00
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-- definition Hom (C : Category) : Cᵒᵖ ×c C ⇒ type :=
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-- functor.mk (λ a, hom (pr1 a) (pr2 a))
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-- (λ a b f h, pr2 f ∘ h ∘ pr1 f)
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-- (λ a, funext (λh, !id_left ⬝ !id_right))
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-- (λ a b c g f, funext (λh,
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-- show (pr2 g ∘ pr2 f) ∘ h ∘ (pr1 f ∘ pr1 g) = pr2 g ∘ (pr2 f ∘ h ∘ pr1 f) ∘ pr1 g, from sorry))
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2014-10-09 05:57:41 +00:00
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--I'm lazy, waiting for automation to fill this
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2014-11-04 00:22:30 +00:00
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variables (C D : Category)
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2014-10-09 05:57:41 +00:00
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2014-11-04 00:22:30 +00:00
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-- private definition aux_prod_cat [instance] : category (obD × obD) := prod_category (opposite.opposite D) D
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2014-10-12 20:06:00 +00:00
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2014-11-04 00:22:30 +00:00
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-- definition adjoint.{l} (F : C ⇒ D) (G : D ⇒ C) :=
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-- --@natural_transformation _ Type.{l} (Dᵒᵖ ×c D) type_category.{l+1} (Hom D) (Hom D)
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-- sorry
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--(@functor.compose _ _ _ _ _ _ (Hom D) (@product.prod_functor _ _ _ _ _ _ (Dᵒᵖ) D sorry sorry))
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2014-10-09 06:44:09 +00:00
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--(Hom C ∘f sorry)
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2014-10-09 07:05:37 +00:00
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--product.prod_functor (opposite.opposite_functor F) (functor.ID D)
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2014-10-09 05:57:41 +00:00
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end adjoint
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