Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorceciliaflori
    • CommentTimeAug 14th 2013



    be a commutative square of categories and functors. Assume that L 1L_1 and L 2L_2 have right adjoints R 1R_1 and R 2R_2, respectively. Under which conditions do we have FR 1R 2GFR_1\cong R_2G?

    The thing is that we have a concrete situation in which this does seem to be the case, but we would like to have an easy-to-check criterion which implies it.

    In our case, all four categories are actually functor categories and the right adjoints correspond to taking Kan extensions.

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 14th 2013

    Hi Cecillia,

    the phrase Beck-Chevalley condition is what you are looking for. Proposition 1 at that page is an example similar to your case. (BTW, nice to meet you in Sydney)

    • CommentRowNumber3.
    • CommentAuthorceciliaflori
    • CommentTimeAug 15th 2013

    Hi :)

    thanks for the link, it is right to the point!

    Looks like the pullbacks of opfibrations example in the nLab might apply to the case we are considering.