Composition for non-aqueous secondary battery functional layer, battery member for non-aqueous secondary battery, method of producing laminate for non-aqueous secondary battery, and non-aqueous secondary battery

A composition for a non-aqueous secondary battery functional layer, comprising a particulate polymer, wherein

• the particulate polymer has a core-shell structure including a core portion and a shell portion covering at least a portion of an outer surface of the core portion,
• the particulate polymer has a volume-average particle diameter of not less than 0.05 μm and not more than 1.5 μm,
• the core portion is formed of a polymer A including an aromatic vinyl monomer unit, having a degree of swelling in electrolyte solution of 400 mass % or less, and having a glass-transition temperature of 25° C. or higher, and
• the shell portion is formed of a polymer B including not less than 1 mol % and not more than 30 mol % of a sulfo group-containing monomer unit, wherein the sulfo group-containing monomer unit is a lithium styrene sulfonate unit.