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Pullback-Flat Acts are Strongly Flat

Published online by Cambridge University Press:  20 November 2018

Sydney Bulman-Fleming
Sydney Bulman-Fleming*
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5
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Abstract

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Let 5 be a monoid. A right S-system A is called strongly flat if the functor A ⊗ — (from the category of left S-systems into the category of sets) preserves pullbacksand equalizers. (This concept arises in B. Stenström, Math. Nachr. 48(1971), 315-334 under the name weak flatness). The main result of the present paper is a proof that for A to be strongly flat it is in fact sufficient that A ⊗ — preserve only pullbacks. The approach taken is to develop an "interpolation" condition for pullback-preservation, and then to show its equivalence to Stenström's conditions for strong flatness.

Keywords

20M1020M50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 4 , 01 December 1991 , pp. 456 - 461
Copyright
Copyright © Canadian Mathematical Society 1991

References

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