nLab inert morphism




A morphism in FinSet */FinSet^{*/} is called an inert morphism if it is surjective and an injection on those elements that are not sent to the base point.

A morphism in FinSet */FinSet^{*/} is called an active morphism if only the basepoint goes to the basepoint.

(Lurie, def., def.

See at (infinity,1)-operad


Factorization system

(Inert,Active)(Inert, Active) is an orthogonal factorization system on FinSet */FinSet^{*/}.

(Lurie, remark

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