Binder composition for secondary battery, slurry composition for secondary battery, functional layer for secondary battery, separator for secondary battery, electrode for secondary battery, and secondary battery

A binder composition for a secondary battery comprising a polymer and a solvent, wherein

• the polymer is core-shell particles including a core portion formed of a polymer (a1) and a shell portion formed of a polymer (a2),
• the polymer (a2) includes:
• not less than 50.0 mass % and not more than 89.9 mass % of a monofunctional unsaturated carboxylic acid ester monomer unit;
• not less than 10.0 mass % and not more than 49.9 mass % of at least one type of monomer unit selected from a monofunctional unsaturated carboxylic acid monomer unit and a monofunctional unsaturated sulfonic acid monomer unit;
• not less than 0.1 mass % and not more than 10.0 mass % of a monomer unit of a monomer including at least two vinyl functional groups;
• and 5.0 mass % or less of an aromatic vinyl monomer unit, and
• the at least one type of monomer unit selected from a monofunctional unsaturated carboxylic acid monomer unit and a monofunctional unsaturated sulfonic acid monomer unit is not less than 0.1 mol and not more than 15,000 mol relative to 1 mol of the monomer unit of the monomer including at least two vinyl functional groups.