Decidable object in a topos
= Decidable object in a topos
{title2=$A^2=\Delta_A\amalg D_A$}
An object is decidable when its diagonal is a complemented <subobject> of its square. Equivalently its internal equality is decidable. Pullback gives closure under subobjects; coordinatewise equality gives closure under finite products. For an existing coproduct, unequal summands together with the complements of the diagonal in each equal summand form the diagonal complement.