# Intuition for cofibration

The notion of a fibration has a nice geometric intuition of one topological space (a fiber) being parametrized by another topological space (the base) -- this is taken from the Wikipedia entry on Fibration.

Now, I would like to know if there is an analogous geometric picture for the situation of cofibrations. Like that of a parametrized inclusion of a space into another space (apologies if this is nonsense).

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In this setup, if a fiber sequence $X \rightarrow Y \rightarrow Z$ is trivial (so $Y \simeq X \times Z$) then the connecting maps in homotopy will be trivial; dually, if a cofiber sequence $A \rightarrow B \rightarrow C$ is trivial (so $C \simeq B \vee \Sigma A$) then the connecting maps in cohomology will be trivial. I think these facts get at what you're asking. –  Aaron Mazel-Gee Nov 15 '12 at 1:29