Categories with Duals
July 7, 2007  Posted by John Armstrong  Category theory
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It looks like you’ve got some misplaced dollar signs in the penultimate paragraph, after “so that we can just use “.
Comment by Blake Stacey  July 8, 2007 
Thanks, fixed.
Comment by John Armstrong  July 8, 2007 
[…] this sort of naturality before, though. If we read the diagram in , consider a monoidal category with duals, and use the functor , then this is exactly the sort of naturality we find in the duality arrows […]
Pingback by Extraordinary Naturality « The Unapologetic Mathematician  August 30, 2007 
[…] Another thing vector spaces come with is duals. That is, given a vector space we have the dual vector space of “linear functionals” […]
Pingback by Dual Spaces « The Unapologetic Mathematician  May 27, 2008 
[…] category of matrices also has duals. In fact, each object is selfdual! That is, we set . We then need our arrows and […]
Pingback by The Category of Matrices II « The Unapologetic Mathematician  June 3, 2008 
typoes in par 4: for every f:N>M an arrow f^*:M*>N*
Comment by Avery Andrews  July 19, 2008 
Thanks.
Comment by John Armstrong  July 19, 2008 
[…] of a bialgebra is monoidal. What do we get for Hopf algebras? What does an antipode buy us? Duals! At least when we restrict to finitedimensional […]
Pingback by Representations of Hopf Algebras I « The Unapologetic Mathematician  November 12, 2008 
[…] Okay, I noticed that I never really gave the definition of the coevaluation when I introduced categories with duals, because you need some linear algebra. Well, now we have some linear algebra, so let’s do […]
Pingback by The Coevaluation on Vector Spaces « The Unapologetic Mathematician  November 13, 2008 
[…] if that weren’t enough, has duals! Indeed, we have a cone in the dual vector space defined by if and only if for all . Or in other […]
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