Irreducible object in a topos
= Irreducible object in a topos
A noninitial object is irreducible, or supercompact, when every family of subobjects with union the whole object contains the whole object as one member. This concerns unions of subobjects rather than disjoint coproduct decompositions. <Irreducible representable sheaves for the regular coverage> follow from the one-arrow nature of that coverage.