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

(Lurie, def. 2.1.1.8, def. 2.1.2.1).

See at *(infinity,1)-operad*

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

Last revised on February 2, 2015 at 12:57:33. See the history of this page for a list of all contributions to it.