Add(M) lies in Prod(M) exactly for Sigma-pure-injective objects under a non-omega-measurable cardinality hypothesis, and Prod(M)=Add(M) exactly for Sigma-pure-injective product-rigid objects, in two broad categorical settings.
Bennett-Tennenhaus, Characterisations of Σ -pure-injectivity in triangulated categories and applications to endoperfect objects , Fund
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
citation-role summary
background 1
citation-polarity summary
fields
math.CT 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$
Add(M) lies in Prod(M) exactly for Sigma-pure-injective objects under a non-omega-measurable cardinality hypothesis, and Prod(M)=Add(M) exactly for Sigma-pure-injective product-rigid objects, in two broad categorical settings.