Re: How can we have a categorical definition of "theory"

In what way is defining a theory dependent on defining a sentence? There are lots of categorical definitions of theories of various sorts: Operads, PROPs, Lawvere theories,..., even monads. One of the points of category theory, esp. higher category theory, has been to liberate mathematical thought from being bound to strings of symbols like terms and sentences. Best Thougths, David Yetter Professor of Mathematics Kansas State University [For admin and other information see: http://www.mta.ca/~cat-dist/ ]