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productivity; topological group; coreflective class
Every nontrivial countably productive coreflective subcategory of topological linear spaces is $\kappa$-productive for a large cardinal $\kappa$ (see [10]). Unlike that case, in uniform spaces for every infinite regular cardinal $\kappa$, there are coreflective subcategories that are $\kappa$-productive and not $\kappa^+$-productive (see [8]). From certain points of view, the category of topological groups lies in between those categories above and we shall show that the corresponding results on productivity of coreflective subcategories are also ``in between'': for some coreflections the results analogous to those in topological linear spaces are true, for others the results analogous to those for uniform spaces hold.
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