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Proceedings of the American Mathematical Society
Journal Article

Embedding of Categories

Michael Barr
Proceedings of the American Mathematical Society
Vol. 37, No. 1 (Jan., 1973), pp. 42-46
Published by: American Mathematical Society
DOI: 10.2307/2038702
https://www.jstor.org/stable/2038702
Page Count: 5

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Topics: Functors, Mathematical theorems, Embeddings, Topology
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Embedding of Categories
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Abstract

In this paper we generalize the notion of exact functor to an arbitrary category and show that every small category has a full embedding into a category of all set-valued functors on some small category. The notion of exact is such that this result generalizes the author's exact embedding of regular categories and, indeed, Mitchell's embedding of abelian categories. An example is given of the type of diagram-chasing argument that can be given with this embedding.
Proceedings of the American Mathematical Society © 1973 American Mathematical Society