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Modules commuting (via Hom) with some colimits. (English) Zbl 1080.16504
Summary: For every module \(M\) we have a natural monomorphism \[ \Psi\colon\coprod_{i\in I}\operatorname{Hom}_R(M,A_i)\to\operatorname{Hom}_R\Bigl(M,\coprod_{i\in I}A_i\Bigr) \] and we focus our attention on the case when \(\Psi\) is also an epimorphism. Some other colimits are also considered.

MSC:
16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras
18A35 Categories admitting limits (complete categories), functors preserving limits, completions
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