For an arbitrary infinite cardinal κ, we define classes of κ-cslender and κ-tslender modules as well as related classes of κ-hmodules and initiate a study of these classes.

• 03C20 - Ultraproducts and related constructions
• 03E10 - Ordinal and cardinal numbers
• 16D80 - Other classes of modules and ideals in associative algebras
• 18A20 - Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
• 20K25 - Direct sums, direct products, etc. for abelian groups