Thus a stack is formally given as a fibred category over another " base " category, where the base has a Grothendieck topology and where the fibred category satisfies a few axioms that ensure existence and uniqueness of certain gluings with respect to the Grothendieck topology.
22.
It was here that Seifert submitted his dissertation, " Topologie 3-dimensionaler gefaserter R�ume " ( Topology of 3-dimensional fibred spaces ), on 1 February 1932, and he was awarded with this doctorate of philosophy after his oral examination on March 3.
23.
If " E " has a terminal object " e " and if " F " is fibred over " E ", then the functor ? from cartesian sections to " F e " defined at the end of the previous section is an equivalence of categories and moreover surjective on objects.
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