Geodesic
Pullback-Flat Acts are Strongly Flat
Canadian mathematical bulletin, Tome 34 (1991) no. 4, pp. 456-461

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DOI

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.
DOI : 10.4153/CMB-1991-073-2
Mots-clés : 20M10, 20M50 
Bulman-Fleming, Sydney. Pullback-Flat Acts are Strongly Flat. Canadian mathematical bulletin, Tome 34 (1991) no. 4, pp. 456-461. doi: 10.4153/CMB-1991-073-2
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     title = {Pullback-Flat {Acts} are {Strongly} {Flat}},
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     year = {1991},
     volume = {34},
     number = {4},
     doi = {10.4153/CMB-1991-073-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-073-2/}
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