The Unapologetic Mathematician

Mathematics for the interested outsider

Categories with Duals

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July 7, 2007 - Posted by | Category theory


  1. It looks like you’ve got some misplaced dollar signs in the penultimate paragraph, after “so that we can just use \eta_M“.

    Comment by Blake Stacey | July 8, 2007 | Reply

  2. Thanks, fixed.

    Comment by John Armstrong | July 8, 2007 | Reply

  3. […] 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 | Reply

  4. […] 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 | Reply

  5. […] category of matrices also has duals. In fact, each object is self-dual! That is, we set . We then need our arrows and […]

    Pingback by The Category of Matrices II « The Unapologetic Mathematician | June 3, 2008 | Reply

  6. typoes in par 4: for every f:N->M an arrow f^*:M*->N*

    Comment by Avery Andrews | July 19, 2008 | Reply

  7. Thanks.

    Comment by John Armstrong | July 19, 2008 | Reply

  8. […] 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 finite-dimensional […]

    Pingback by Representations of Hopf Algebras I « The Unapologetic Mathematician | November 12, 2008 | Reply

  9. […] 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 | Reply

  10. […] 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 […]

    Pingback by Ordered Linear Spaces II « The Unapologetic Mathematician | May 15, 2009 | Reply

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