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Essential geometric morphisms between toposes over finite sets

Published online by Cambridge University Press:  24 October 2008

John Haigh
John Haigh
Affiliation:
University of Durham
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Extract

We show that if {Gi}J ε I is a generating set for an (elementary) topos ℰ then {P(Gi)}iεI is a cogenerating set for x2130;. From this we show that if topos ℰ contains an object G whose subobjects generate ℰ, then ΩG is a cogenerator for ℰ. Let denote the topos of finite sets and functions. We also show that if ℰ1 is a topos and ℰ2 is a bounded -topos then every geometric morphism ℰ1 → ℰ2 is essential.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 1 , January 1980 , pp. 21 - 24
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

REFERENCES

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