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Images in Topoi

Published online by Cambridge University Press:  20 November 2018

K. A. Rowe
K. A. Rowe*
Affiliation:
Department of Mathematics University of Waterloo, Waterloo, Ontario
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The construction of images of morphisms in an elementary topos E has hithero required the use of colimits. For example, in [1], Freyd constructs the image of a morphism by taking the equalizer of the cokernel pair of the morphism. In particular, the construction of the direct image functor, or, as it is sometimes referred to, existential quantification along a morphism, has required the use of images, and hence colimits. However, Mikkelsen has defined existential quantification using only limits.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 4 , 01 December 1977 , pp. 471 - 478
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Freyd, P., Aspects of Topoi. Bull. Australian Math. Soc, Vol. 7 (1972).Google Scholar
2. Kock, A., Lecouturier, P., and Mikkelsen, C., Some Topos-theoretic Concepts of Finiteness. Aarhus University Preprint Series No. 29 (1974).Google Scholar
3. Rowe, K.A., Topoidal Set Theory. University of Waterloo, Dec. (1974).Google Scholar