# Equi-existence of (co)products

Inspired by this question, does anyone know the strongest condition that ensures a category has sums if and only if it has products. What of other (co)limits?

• "Weakest" implies the set of such conditions should be directed under implication, which is probably false. One nice condition that implies products and coproducts appear simultaneously is preadditivity. – Kevin Carlson Sep 24 '16 at 1:02
• Sure, you stated it in your question: "it has products iff it has coproducts". That's literally by definition the "weakest" condition. – Najib Idrissi Sep 24 '16 at 9:40