We all know about group algebras, and this leads naturally to the idea of a category algebra: form a vector space having as a basis the morphisms in a given category, with the obvious product (taking the product of two morphisms to be zero if the head of one isn't the tail of the other). I used an example of this in my paper "Quantum Gravity and the Algebra of Tangles," but I have never seen a reference to the general concept, and I would appreciate one. What I am now interested in, however, is generalizing this notion to 2-category algebras. This might be related to recent algebraic work of Ruth Lawrence, which I haven't actually seen. Any leads? Regards, John Baez
On John Baez's question: I don't know of any linearization of 2-categories, but the "category algebra" construction gives examples of what Barry Mitchell (old work! -- dare one say classical category theory?) called "algebroids". I don't know the reference, but someone else can certainly recall it. --David Yetter +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
... what Barry Mitchell (old work! -- dare one say classical category theory?) called "algebroids". I don't know the reference ...
?? "Rings with several objects", Advances in Mathematics 8 (72) 1-161 Steve Vickers. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
participants (3)
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baez＠ucrmath.ucr.edu -
dyetter＠math.ksu.edu -
sjv＠doc.ic.ac.uk