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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Note on the projective limit on small categories


Author: Olav Arnfinn Laudal
Journal: Proc. Amer. Math. Soc. 33 (1972), 307-309
MSC: Primary 18A30
MathSciNet review: 0291241
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Abstract: Let X be a small category and let $ {\mathbf{A}}{{\mathbf{b}}^X}$ be the category of covariant functors on X with values in Ab. Consider the projective limit functor proj $ {\lim _X}:{\mathbf{A}}{{\mathbf{b}}^X} \to {\mathbf{Ab}}$. The categories X for which proj $ {\lim _X}$ is exact are characterized, proving a conjecture of Oberst.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0291241-8
PII: S 0002-9939(1972)0291241-8
Keywords: Category of functors, projective limit, cohomologically trivial monoid, cohomologically trivial group
Article copyright: © Copyright 1972 American Mathematical Society