Maps (morphisms) play a central role in modern
mathematics.
After studying basic properties of continuous maps
and homotopies, the next subject to study in algebraic
topology would be various kinds of fibrations, such as
covering spaces, fiber bundles, Serre and Hurewicz
fibration, quasifibrations.
The dual notion, cofibrations, might look unnatural
at first. One of the ways to understand its importance
is to study
model categories
.
