[Agda] Tips for working around proof relevance

[Thorsten Altenkirch]

But this is not the arrow category it is something else. 

If you want to implement category theory you need to work with a type theory with a reasonable notion of equality. Setoids are a bad idea because you never hide implementation details. You also want to be able to transport properties among equal elements.

The message is simple: don't program in assembly language.

Thorsten

On 16/12/2020, 12:35, "Agda on behalf of James Wood" <agda-bounces at lists.chalmers.se on behalf of james.wood.100 at strath.ac.uk> wrote:

    On 16/12/2020 07:36, Thorsten Altenkirch wrote:
    > But then how do you construct the arrow category? 

    The canonical answer to questions like this is to look in 
    agda-categories, and see what it does.

    In this case 
    (https://github.com/agda/agda-categories/blob/master/src/Categories/Category/Construction/Arrow.agda), 
    it looks like when we make the type of objects of the arrow category, we 
    just forget the equivalence relation on the hom-setoid. Objects of the 
    arrow category (A, B, f) and (A, B, f′) where f ≈ f′ are isomorphic, 
    which should be good enough because we never talk about equality on 
    objects. The answer to the original question about comma categories 
    should be very similar.

    Best regards,
    James
    _______________________________________________
    Agda mailing list
    Agda at lists.chalmers.se
    https://lists.chalmers.se/mailman/listinfo/agda




This message and any attachment are intended solely for the addressee
and may contain confidential information. If you have received this
message in error, please contact the sender and delete the email and
attachment. 

Any views or opinions expressed by the author of this email do not
necessarily reflect the views of the University of Nottingham. Email
communications with the University of Nottingham may be monitored 
where permitted by law.