Re: categories of models of cartesian PROPs

[Fabio Gadducci <fabio.gadducci@unipi.it>]

Dear John,

do not know if it may be useful, but you can say a few interesting things wrt. models if each object of the prop T has just a co-monoid structure (w/o being natural). In fact, you may e.g. capture partial functions and relational algebras.

Some details in Corradini-Gadducci, A functorial semantics for multi-algebras and partial algebras. TCS 286(2): 293-322 (2002).

Best, Fabio

> On 22/ago/2015, at 03:49, John Baez <baez@math.ucr.edu> wrote:
> 
> Hi -
> 
> I was reassured by a decategorified analogue: if T and C are commutative
>> monoids and we make the set of monoid homomorphism T -> C into a
>> commutative monoid by pointwise multiplication, any one-variable identity
>> (like x^2 = x) obeyed by* either C or T*  will be inherited by
>> CommMon[T,C].
>> 
> 
> It seems that italicized text gets transmogrified here.  I meant:
> 
> any one-variable identity (like x^2 = x) obeyed by either C or T will be
>> inherited by CommMon[T,C].
>> 
> 
> Best,
> jb



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