nLab
cofiber

Definition

Lemma

For $f:A\to B$ a morphism in a category with a terminal object, the cofiber of $f$ is the cofiber coproduct of $f$ with the terminal morphism, hence the pushout

$$\begin{array}{ccc}A& \stackrel{f}{\to }& B\\ \downarrow & & \downarrow \\ *& \to & B\coprod _A*\end{array}.$$\array{ A &\stackrel{f}{\to}& B \\ \downarrow && \downarrow \\ * &\to& B \coprod_A * } \,.

Examples

Cokernels

In an additive category cofibers over the zero object are called cokernels.

Related concepts

• fiber, homotopy fiber, fiber sequence

• homotopy cofiber

• kernel, cokernel