Suppose D is a finite category. Does there exist a unique discrete opfibration (dof) p:D->C such that C has a minimal number of objects? (With "unique", I mean that any two dofs p:D->C and p':D->C', where C and C' have the minimal number of objects, are isomorphic in the sense that there exists an isomorphism i:C->C' such that p' = ip) If so, is there an efficient algorithm to compute this discrete opfibration? If not so, can you give a counter-example? Thanks in advance for any replies, Frank Piessens Katholieke Universiteit Leuven. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Let C be a category with 2 objects A,B and 2 morphisms u,v:A->B. let D be the binary copower of C, i.e. the product of C with the 2-object discrete category and let F:D->C be the codiagonal funjctor mapping both copies of C identically to C. Let G:C->D be the functor mpping one coy of C identically and interchanging u and v in the other copy. Then F and G are opfibations, which are not isomorphic under D (though they are isomorphic over C). Greetings Reinhard Boerger ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
participants (2)
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Frank.Piessens@cs.kuleuven.ac.be -
Reinhard.Boerger@FernUni-Hagen.de