University of Oxford Logo University of OxfordDepartment of Computer Science - Home
On Facebook
Facebook
Follow us on twitter
Twitter
Linked in
Linked in
Flickr
Flickr
Google plus
Google plus
Digg
Digg
Pinterest
Pinterest
Stumble Upon
Stumble Upon

Oxford Quantum Talks Archive

Principally-generated modules on a quantale

Isar Stubbe, University of Antwerp
Categories, Logic and Foundations of Physics IV, January 2009, Imperial College London

Let [[$ Q $]] be a quantale, and [[$ \rm{Mod}(Q) $]] the locally ordered category of [[$ Q $]]-modules and [[$ Q $]]-module morphisms. Using splittings of idempotents and adjunctions in [[$ \rm{Mod}(Q) $]], I shall define the 'principal elements' of a given [[$ Q $]]-module; a 'principally generated' [[$ Q $]]-module is then one "with enough principal elements". Applying this to a module over the two-element chain, i.e. a complete lattice, will give a familiar notion. I shall explain how, in general, this is related to the theory of ordered (!) sheaves over [[$ Q $]]. When [[$ Q $]] is moreover involutive, it makes sense to speak of `principally symmetric' [[$ Q $]]-modules; this then is related to sheaves over [[$ Q $]]. Time permitting, I shall say a word or two on 'Hilbert [[$ Q $]]-modules' too.

[video] [streaming video]