[Haskell-cafe] Categorical description of systems with dependent types

Iavor Diatchki iavor.diatchki at gmail.com
Thu Dec 2 18:19:56 CET 2010

Bart Jacobs's book "Categorical Logic and Type Theory" has a
categorical description of a system with dependent types (among
others).  The book is fairly advanced but it has lots of details about
the constructions.
Hope this helps,

On Thu, Dec 2, 2010 at 8:18 AM,  <roconnor at theorem.ca> wrote:
> On Thu, 2 Dec 2010, Petr Pudlak wrote:
>> Hi,
>> recently, I was studying how cartesian closed categories can be used to
>> describe typed functional languages. Types are objects and morphisms are
>> functions from one type to another.
>> Since I'm also interested in systems with dependent types, I wonder if
>> there is a categorical description of such systems. The problem (as I see
>> it) is that the codomain of a function depends on a value passed to the
>> function.
>> I'd happy if someone could give me some pointers to some papers or other
>> literature.
> Voevodsky talks about the category of contexts in
> <http://www.mefeedia.com/watch/31778282>, which I understand is described in
> more detail in "Semantics of type theory : correctness, completeness, and
> independence results" by Thomas Streicher.
> --
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