lean2/library/algebra/category/limit.lean

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-- 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
import .basic
import data.sigma
open eq eq.ops category functor natural_transformation
namespace limits
--representable functor
section
parameters {obI ob : Type} {I : category obI} {C : category ob} {D : I ⇒ C}
definition constant_diagram (a : ob) : I ⇒ C :=
mk (λ i, a)
(λ i j u, id)
(λ i, rfl)
(λ i j k v u, symm !id_compose)
definition cone := Σ(a : ob), constant_diagram a ⟹ D
-- definition cone_category : category cone :=
-- mk (λa b, sorry)
-- (λ a b c g f, sorry)
-- (λ a, sorry)
-- (λ a b c d h g f, sorry)
-- (λ a b f, sorry)
-- (λ a b f, sorry)
end
end limits
-- functor.mk (λ a, sorry)
-- (λ a b f, sorry)
-- (λ a, sorry)
-- (λ a b c g f, sorry)