Algebraic Topology · Problem 4H.2

Homotopy Theory — Allen Hatcher

Mathematics — Topology · eckmann-hilton-duality

Problem

Consider a pushout diagram as at the right, where

B \sqcup_f X

B

with

X

attached along

A

via

f

. Show that if

A \hookrightarrow X

is a cofibration, so is

B \hookrightarrow B \sqcup_f X

\begin{array}{ccc} A & \xrightarrow{f} & B \\ \downarrow & & \downarrow \\ X & \longrightarrow & B \sqcup_f X \end{array}