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charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Dear Colleagues: This is surely something well-known, but it is also opaque to search-engine= queries. It is well-known (and I've both used the result and proved it by= hand) than group objects in Cat and category object in Groups are the same= thing: strict monoidal categories in which every object and every arrow h= ave an inverse with respect to \otimes. What class of theories (e.g. finite product, left-exact, finitely axiomatiz= able equational,...) have the property that category objects in their categ= ory of models are the same as models of the theory in Cat? Citations would= be welcomed. The question came up in work with an old student of mine, and rather than s= pending time proving the result we'd like for the particular theory at hand= , I thought it best to see if it followed from something in the literature.= Alas, all sensible keyword combinations give pages of irrelevant search r= esults, so asking the community seemed the best way to proceed. Thanks in advance. Best thoughts, D.Y. You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message. View group files | Leave group | = Learn more about Microsoft 365 Groups --_000_SN6PR05MB5213969D388EA39F22C1C72CA2322SN6PR05MB5213namp_ Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable
Dear Colleagues:

This is surely something well-known, but it is also opaque to search-engine= queries.  It is well-known (and I've both used the result and proved = it by hand) than group objects in Cat and category object in Groups are the= same thing:  strict monoidal categories in which every object and every arrow have an inverse with respect to \oti= mes.

What class of theories (e.g. finite product, left-exact, finitely axiomatiz= able equational,...) have the property that category objects in their categ= ory of models are the same as models of the theory in Cat?  Citations = would be welcomed.

The question came up in work with an old student of mine, and rather than s= pending time proving the result we'd like for the particular theory at hand= , I thought it best to see if it followed from something in the literature.=   Alas, all sensible keyword combinations give pages of irrelevant search results, so asking the community seemed th= e best way to proceed.

Thanks in advance.

Best thoughts,
D.Y.
 
 
You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message.
 
View group files   |   Leav= e group   |&n= bsp;  Learn more about Microsoft 365 Groups
 
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