Finish non-dep functoriality of adjoints

With some help from Mike Shulman on #627 and #629, I've managed to
finish the construction that shows that the construction of adjoint
functors is functorial in its functor argument.  I've not yet managed to
extend this to the dependent case as an assembled functor, though the
individual parts all have dependent versions.

This closes #629.
Thanks! Could you report this as a documentation bug ?
I could do it myself too, but you may have more information.
There is a bit in ./refman/RefMan-cic.tex in trunk, but apparently not in
the index.

On Sun, Dec 21, 2014 at 8:10 PM, Jason Gross <notifications@github.com>
wrote:

> In theories/categories/Adjoint/Functorial/Core.v
> <https://github.com/HoTT/HoTT/pull/648#discussion-diff-22149506>:
>
> > @@ -0,0 +1,63 @@
> > +(** * Functoriality of the construction of adjunctions *)
> > +Require Import Category.Core Functor.Core NaturalTransformation.Core.
> > +Require Import Functor.Identity Functor.Composition.Core.
> > +Require Import Category.Dual.
> > +Require Import FunctorCategory.Core.
> > +Require Import Category.Sigma.OnObjects Category.Prod.
> > +Require Import Adjoint.Core Adjoint.UnitCounit Adjoint.Dual.
> > +Require Import Adjoint.Functorial.Parts Adjoint.Functorial.Laws.
> > +Require Import HoTT.Types.Prod.
> > +
> > +Set Universe Polymorphism.
> > +Set Implicit Arguments.
> > +Generalizable All Variables.
> > +Set Asymmetric Patterns.
>
> It a compatibility command that allows the old-style match-statement. In
> 8.4, the default was to not permit the parameters to show up in the
> arguments (so cons took two arguments and nil took zero), and in trunk,
> the default is to require the extra parameters:
>
> Inductive list A := nil | cons (x : A) (xs : list A).
> Unset Asymmetric Patterns.Definition behead {A} (ls : list A)
>   := match ls with
>        | nil _ => nil _
>        | cons _ x xs => xs
>      end.Set Asymmetric Patterns.Definition behead' {A} (ls : list A)
>   := match ls with
>        | nil => nil _
>        | cons x xs => xs
>      end.
>
> Since this is given as a compatibility option, it's possible that (perhaps
> when we clean up to make an 8.5 release) we should strip this option and
> adjust all of the explicit matches.
>
> The reason it shows up at the top of files like this was that I'm keeping
> the styles of the categories files to put these settings at the top of each
> file. It's sufficient to globally set them once at the top of
> categories/Category/Core.v.
>
> —
> Reply to this email directly or view it on GitHub
> <https://github.com/HoTT/HoTT/pull/648/files#r22149506>.
>