Re: How analogous are categorial and material set theories?

[Vaughan Pratt <pratt@cs.stanford.edu>]

I prefer to think of what Steve presumably has in mind here as an
equational theory where composition is 2-ary where 2 is not 1+1 but
rather o--->o.

One difference between equational logic and first order logic is that
only the former has well-defined homomorphisms (not sure if Gerald Sacks
would have agreed).?? Just as group theory (in Steve's sense) has
homomorphisms, so does category theory in that sense have functors.

I'm not sure how one argues that CT has natural transformations
however.?? They seem to enter as part of the metatheory, which as usually
presented seems to be pretty set theoretic in its outlook. How do NT's
look in an HOTT account of CT?

The language of the Big Bang Theory is pretty family-oriented, except
for equality which seems somewhat controversial.?? But I digress.

Vaughan

On 12/07/17 10:49 PM, Steve Vickers wrote:
> Dear Patrik,
>
> The theory of categories is a first order theory, so what exactly are you denying here?
>
> Steve.
>
>> On 7 Dec 2017, at 18:58, peklund@cs.umu.se wrote:
>>
>> Is Category Theory a Theory? I think not. At least not in a logical
>> sense.
>>
>
>
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