Hi Bill,

On 2015-10-01, Bill Page <bill.p...@newsynthesis.org> wrote:
>> I would expect that somebody who doesn't know category theory (the
>> mathematical area) would find the category framework in Sage very
>> confusing, just like somebody who doesn't know calculus might find the
>> symbolic functionality confusing.
>
> No, I find the Sage implementation of these ideas confusing, or at the
> very least overly complicated.

Indeed, when William states that someone who doesn't know category theory
mathematically might find Sage's category framework confusing, one can as
well state: Someone who has a profound knowledge about the mathematical
implications of category theory will be very confused by how Sage's
category framework works.

I am attending the annual meeting of a priority programme of German
science foundation, and there has also been a talk about CAP. It seems
to me that they really mean business with a constructive approach towards
category theory: When the user provides a construction algorithm for each
existence quantor appearing in the axioms (say, given a morphism one has
functions returning the kernel and its embedding into the domain, and
a function that returns, for each test object, the morphism whose
existence is granted by the universal property of the kernel), then CAP
will help you with things like connecting homomorphisms or spectral
sequences.

When I first encountered Sage's category framework, I expected to see something
similar to what we now have in CAP, but it has in fact a rather
different flavour and purpose.

Best regards,
Simon


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