Geodesic
On the object-wise tensor product of functors to modules
Theory and applications of categories, Tome 7 (2000), pp. 226-235.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We investigate preserving of projectivity and injectivity by the object-wise tensor product of $R\Bbb{C}$-modules, where $\Bbb{C}$ is a small category. In particular, let ${\cal O}(G,X)$ be the category of canonical orbits of a discrete group $G$, over a $G$-set $X$. We show that projectivity of $R{\cal O}(G,X)$-modules is preserved by this tensor product. Moreover, if $G$ is a finite group, $X$ a finite $G$-set and $R$ is an integral domain then such a tensor product of two injective $R{\cal O}(G,X)$-modules is again injective.
Classification : Primary 18G05, secondary 16W50, 55P91.
Keywords: category of canonical orbits, injective (projective) RC-module, linearly compact k-module, tensorpr oduct. 
@article{TAC_2000_7_a10,
     author = {Marek Golasinski},
     title = {On the object-wise tensor product of functors to modules},
     journal = {Theory and applications of categories},
     pages = {226--235},
     publisher = {mathdoc},
     volume = {7},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2000_7_a10/}
}
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Marek Golasinski. On the object-wise tensor product of functors to modules. Theory and applications of categories, Tome 7 (2000), pp. 226-235. http://geodesic.mathdoc.fr/item/TAC_2000_7_a10/