Category theory MOC

Simple object

Let be a category. An object is called simple iff its only quotients (in the sense of coëqualizers) are the terminal object and itself.¹ #m/def/cat If is abelian category, it is sufficient for to have no subobjects.

Examples

• Simple group in .
• Simple module in .
• Simple ring in .

Properties

• Schur's lemma in abelian categories

See also

• Semisimple object in an abelian category

#state/tidy | #lang/en | #SemBr