Re: How can we have a categorical definition of "theory"
Dear Patrik, It's absolutely vital to Grothendieck's idea of toposes as generalized spaces. It's essentially categorical logic that allows you to think of toposes as spaces and geometric morphisms as continuous maps. For an introduction, see my TACL talks http://www.cs.bham.ac.uk/~sjv/talks.php particularly numbers 1-4 (the Olomouc tutorials). Steve. On 10/11/2017 16:49, peklund@cs.umu.se wrote:
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Categorical "logic" in a topos to me makes no practical sense at all.
Patrik
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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/ ]
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David Yetter -
Steve Vickers