Dear Bill, I jsut read these posts to learn more :-\
> Granted. "constructive part" was meant to soften my claim. Sure, I wanted just to point out that 'constructive' (in a topos valid sense) is not the same as constructable (in an implementation sense in a CAS). > Yes, elementary topos. I am interested only in the axioms which are > intended to capture set theory "algebraically". I am interested in > topos as a foundation in the sense of set theory. Yes, I see that too, but it might not be sufficient. The theory of computability actually needs topology, as you use `continuous'(!) functions to define abstractly what is computable (loosely). So you need a topology on the topos too, which renders it to be a Grothendieck topos in general. For my current work I would be greatly interested in some computation in a CAS about topos theory. (Actually currently in a 2-categorical sense, which startes to get rather unhandy with paper ans pencil (even to draw the diagrams required)). My problem is that some spaces may not have points, so its not so easy to write down sensible equational formulae and let them check. That was teh back ground reason for my comment. > http://arxiv.org/abs/1112.1284 > > Relative Frobenius algebras are groupoids > Chris Heunen, Ivan Contreras, Alberto S. Cattaneo > (Submitted on 6 Dec 2011) I saw Chris giving a talk about this (I guess, as I have not yet read the paper) in Nijmegen on the QLP2011. Indeed I have to read it asap. They were searching for Frobenius algebra structures which are suitable to be defined on an infinite dimensional (Hilbert) space. If you have questions about this, let me know this, but possibly in a private mail, as this is and of-list-topic. Cheers BF. -- % PD Dr Bertfried Fauser % Research Fellow, School of Computer Science, Univ. of Birmingham % Privat Docent: University of Konstanz, Physics Dept <http://www.uni-konstanz.de> % contact |-> URL : http://www.cs.bham.ac.uk/~fauserb/ % Phone : +44-121-41-42795 -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en.
