nLab
inert morphism

Contents

Definition

Definition

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. 2.1.1.8, def. 2.1.2.1).

See at (infinity,1)-operad

Properties

Factorization system

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

(Lurie, remark 2.1.2.2)

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