# Contents

## Definition

###### Definition

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.

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