Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-12T22:26:28.889Z Has data issue: false hasContentIssue false

Perfect categories

Published online by Cambridge University Press:  20 January 2009

John Isbell
Affiliation:
State University of New York at Buffalo, Amherst, New York 14226
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This note extends to categories Fountain's theorem (2) that for a perfect monoid S, every flat S-set is projective. (The converse is known (4).)

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1976

References

REFERENCES

(1) Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. II (Math. Surveys no. 7, Amer. Math. Soc, 1967).Google Scholar
(2) Fountain, J., Perfect semigroups. Proc. Edinburgh Math. Soc. 20 (1976), 8793.CrossRefGoogle Scholar
(3) Grothendieck, A. et Verdier, J. L., Prefaisceaux (Lecture Notes in Mathematics 269, Springer-Verlag, 1972), 1217.Google Scholar
(4) Isbell, J. R., Perfect monoids, Semigroup Forum 2 (1971), 95118.CrossRefGoogle Scholar
(5) Mitchell, B., The dominion of Isbell, Trans. Amer. Math. Soc. 167 (1972), 319331.CrossRefGoogle Scholar
(6) Stenström, B., Flatness and localization over monoids, Math. Nachr. 48 (1971), 315334.CrossRefGoogle Scholar