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Fibrations and Grothendieck topologies

Published online by Cambridge University Press:  17 April 2009

Howard Lyn Hiller
Howard Lyn Hiller
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.
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Given a site T, that is, a category equipped with a fixed Grothendieck topology, we provide a definition of fibration for morphisms of the presheaves on T. We verify that the notion is well-behaved with respect to composition, base change, and exponentiation, and is trivial on the topos of sheaves. We compare our definition to that of Kan fibration in the semi-simplicial setting. Also we show how we can obtain a notion of fibration on our ground site T and investigate the resulting notion in certain ring-theoretic situations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 1 , February 1976 , pp. 111 - 128
Copyright
Copyright © Australian Mathematical Society 1976

References

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