Geodesic
The Category CvD0, N-Cmod and MP
Journal of convex analysis, Tome 8 (2001) no. 2, pp. 555-568.

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This paper deals with the halfing morphism of $Cv_{D_0, N}$-convex modules, where $D_0$ is the semiring of non-negative dyadic rationals, and its use in the explicit construction of the left adjoint to the functor $O_{D_0, N}:D_0\,$-{\bf Mod} $\longrightarrow Cv_{D_0, N}$- {\bf Cmod} that assigns to each $D_0$-module its canonical $Cv_{D_0, N}$-convex module. Furthermore it is shown that $Cv_{D_0, N}$-{\bf Cmod} is isomorphic to the category {\bf MP} of midpoint algebras. 
@article{JCA_2001_8_2_JCA_2001_8_2_a14,
     author = {H. R\"ohrl},
     title = {The {Category} {Cv\protect\textsubscript{D\protect\textsubscript{0},} {N}-Cmod} and {MP}},
     journal = {Journal of convex analysis},
     pages = {555--568},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2001},
     url = {http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a14/}
}
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H. Röhrl. The Category CvD0, N-Cmod and MP. Journal of convex analysis, Tome 8 (2001) no. 2, pp. 555-568. http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a14/