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feat(algebra/category/): minor additions, start on adjunction
2014-10-09 05:57:41 +00:00
-- Copyright (c) 2014 Floris van Doorn. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Floris van Doorn
refactor(library): major changes in the library I made some major changes in the library. I wanted to wait with pushing until I had finished the formalization of the slice functor, but for some reason that is very hard to formalize, requiring a lot of casts and manipulation of casts. So I've not finished that yet. Changes: - in multiple files make more use of variables - move dependent congr_arg theorems to logic.cast and proof them using heq (which doesn't involve nested inductions and fewer casts). - prove some more theorems involving heq, e.g. hcongr_arg3 (which do not require piext) - in theorems where casts are used in the statement use eq.rec_on instead of eq.drec_on - in category split basic into basic, functor and natural_transformation - change the definition of functor to use fully bundled categories. @avigad: this means that the file semisimplicial.lean will also need changes (but I'm quite sure nothing major). You want to define the fully bundled category Delta, and use only fully bundled categories (type and ᵒᵖ are notations for the fully bundled Type_category and Opposite if you open namespace category.ops). If you want I can make the changes. - lots of minor changes
2014-11-04 00:22:30 +00:00
import .constructions
feat(algebra/category/): minor additions, start on adjunction
2014-10-09 05:57:41 +00:00
open eq eq.ops category functor natural_transformation category.ops prod category.product
namespace adjoint
--representable functor
refactor(library): major changes in the library I made some major changes in the library. I wanted to wait with pushing until I had finished the formalization of the slice functor, but for some reason that is very hard to formalize, requiring a lot of casts and manipulation of casts. So I've not finished that yet. Changes: - in multiple files make more use of variables - move dependent congr_arg theorems to logic.cast and proof them using heq (which doesn't involve nested inductions and fewer casts). - prove some more theorems involving heq, e.g. hcongr_arg3 (which do not require piext) - in theorems where casts are used in the statement use eq.rec_on instead of eq.drec_on - in category split basic into basic, functor and natural_transformation - change the definition of functor to use fully bundled categories. @avigad: this means that the file semisimplicial.lean will also need changes (but I'm quite sure nothing major). You want to define the fully bundled category Delta, and use only fully bundled categories (type and ᵒᵖ are notations for the fully bundled Type_category and Opposite if you open namespace category.ops). If you want I can make the changes. - lots of minor changes
2014-11-04 00:22:30 +00:00
definition foo (C : Category) : C ×c C ⇒ C ×c C := functor.id
feat(algebra/category/): minor additions, start on adjunction
2014-10-09 05:57:41 +00:00
refactor(library): major changes in the library I made some major changes in the library. I wanted to wait with pushing until I had finished the formalization of the slice functor, but for some reason that is very hard to formalize, requiring a lot of casts and manipulation of casts. So I've not finished that yet. Changes: - in multiple files make more use of variables - move dependent congr_arg theorems to logic.cast and proof them using heq (which doesn't involve nested inductions and fewer casts). - prove some more theorems involving heq, e.g. hcongr_arg3 (which do not require piext) - in theorems where casts are used in the statement use eq.rec_on instead of eq.drec_on - in category split basic into basic, functor and natural_transformation - change the definition of functor to use fully bundled categories. @avigad: this means that the file semisimplicial.lean will also need changes (but I'm quite sure nothing major). You want to define the fully bundled category Delta, and use only fully bundled categories (type and ᵒᵖ are notations for the fully bundled Type_category and Opposite if you open namespace category.ops). If you want I can make the changes. - lots of minor changes
2014-11-04 00:22:30 +00:00
-- definition Hom (C : Category) : Cᵒᵖ ×c C ⇒ type :=
-- functor.mk (λ a, hom (pr1 a) (pr2 a))
-- (λ a b f h, pr2 f ∘ h ∘ pr1 f)
-- (λ a, funext (λh, !id_left ⬝ !id_right))
-- (λ a b c g f, funext (λh,
-- show (pr2 g ∘ pr2 f) ∘ h ∘ (pr1 f ∘ pr1 g) = pr2 g ∘ (pr2 f ∘ h ∘ pr1 f) ∘ pr1 g, from sorry))
feat(algebra/category/): minor additions, start on adjunction
2014-10-09 05:57:41 +00:00
--I'm lazy, waiting for automation to fill this
refactor(library): major changes in the library I made some major changes in the library. I wanted to wait with pushing until I had finished the formalization of the slice functor, but for some reason that is very hard to formalize, requiring a lot of casts and manipulation of casts. So I've not finished that yet. Changes: - in multiple files make more use of variables - move dependent congr_arg theorems to logic.cast and proof them using heq (which doesn't involve nested inductions and fewer casts). - prove some more theorems involving heq, e.g. hcongr_arg3 (which do not require piext) - in theorems where casts are used in the statement use eq.rec_on instead of eq.drec_on - in category split basic into basic, functor and natural_transformation - change the definition of functor to use fully bundled categories. @avigad: this means that the file semisimplicial.lean will also need changes (but I'm quite sure nothing major). You want to define the fully bundled category Delta, and use only fully bundled categories (type and ᵒᵖ are notations for the fully bundled Type_category and Opposite if you open namespace category.ops). If you want I can make the changes. - lots of minor changes
2014-11-04 00:22:30 +00:00
variables (C D : Category)
feat(algebra/category/): minor additions, start on adjunction
2014-10-09 05:57:41 +00:00
refactor(library): major changes in the library I made some major changes in the library. I wanted to wait with pushing until I had finished the formalization of the slice functor, but for some reason that is very hard to formalize, requiring a lot of casts and manipulation of casts. So I've not finished that yet. Changes: - in multiple files make more use of variables - move dependent congr_arg theorems to logic.cast and proof them using heq (which doesn't involve nested inductions and fewer casts). - prove some more theorems involving heq, e.g. hcongr_arg3 (which do not require piext) - in theorems where casts are used in the statement use eq.rec_on instead of eq.drec_on - in category split basic into basic, functor and natural_transformation - change the definition of functor to use fully bundled categories. @avigad: this means that the file semisimplicial.lean will also need changes (but I'm quite sure nothing major). You want to define the fully bundled category Delta, and use only fully bundled categories (type and ᵒᵖ are notations for the fully bundled Type_category and Opposite if you open namespace category.ops). If you want I can make the changes. - lots of minor changes
2014-11-04 00:22:30 +00:00
-- private definition aux_prod_cat [instance] : category (obD × obD) := prod_category (opposite.opposite D) D
feat(frontends/lean): add '[]' notation for marking arguments where class-instance resolution should be applied
2014-10-12 20:06:00 +00:00
refactor(library): major changes in the library I made some major changes in the library. I wanted to wait with pushing until I had finished the formalization of the slice functor, but for some reason that is very hard to formalize, requiring a lot of casts and manipulation of casts. So I've not finished that yet. Changes: - in multiple files make more use of variables - move dependent congr_arg theorems to logic.cast and proof them using heq (which doesn't involve nested inductions and fewer casts). - prove some more theorems involving heq, e.g. hcongr_arg3 (which do not require piext) - in theorems where casts are used in the statement use eq.rec_on instead of eq.drec_on - in category split basic into basic, functor and natural_transformation - change the definition of functor to use fully bundled categories. @avigad: this means that the file semisimplicial.lean will also need changes (but I'm quite sure nothing major). You want to define the fully bundled category Delta, and use only fully bundled categories (type and ᵒᵖ are notations for the fully bundled Type_category and Opposite if you open namespace category.ops). If you want I can make the changes. - lots of minor changes
2014-11-04 00:22:30 +00:00
-- definition adjoint.{l} (F : C ⇒ D) (G : D ⇒ C) :=
-- --@natural_transformation _ Type.{l} (Dᵒᵖ ×c D) type_category.{l+1} (Hom D) (Hom D)
-- sorry
--(@functor.compose _ _ _ _ _ _ (Hom D) (@product.prod_functor _ _ _ _ _ _ (Dᵒᵖ) D sorry sorry))
fix(library/algebra/category): minor fixes to reflect recent changes, and fix tests
2014-10-09 06:44:09 +00:00
--(Hom C ∘f sorry)
chore(library/algebra/category): add workaround
2014-10-09 07:05:37 +00:00
--product.prod_functor (opposite.opposite_functor F) (functor.ID D)
feat(algebra/category/): minor additions, start on adjunction
2014-10-09 05:57:41 +00:00
end adjoint
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