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A Relationship between Left Exact and Representable Functors

Published online by Cambridge University Press:  20 November 2018

H. B. Stauffer
H. B. Stauffer*
Affiliation:
University of Chicago, Chicago, Illinois University of British Columbia, Vancouver, British Columbia California State College, Hayward, California
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Our aim in this paper is to demonstrate a relationship between left exact and representable functors. More precisely, in the functor category whose objects are the additive functors from the dual of an abelian category 𝔄 to the category of abelian groups and whose morphisms are the natural transformations between them, the left exact functors can be characterized as those equivalent to a direct limit of representable functors taken over a directed class. The proof will proceed in the following manner. Lambek [3] and Ulmer [7] have shown that any functor T in can be expressed as a direct limit of representable functors taken over a comma category. When T is left exact, it is easily observed that this comma category is a filtered category. When T is left exact, it is easily observed that this comma category is a filtered category.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 2 , April 1971 , pp. 374 - 380
Copyright
Copyright © Canadian Mathematical Society 1971

References

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