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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