I tried to understand the definitions of cofibration and fibration through wikipedia. But I didn't get any motivation why such things are important, and through which basic natural question they come?
Also, I saw this first in the book of J. P. May, concise course in algebraic topology. The book explains many terminologies through maps between objects with lack of motivations (in my opinion). Therefore, I next moved to Wiki, but there also, no motivation for it.
I tried to understand them through some analogous definitions in category of module theory, but I didn't succeed.
Q. 1. What is motivation for defining the fibration and cofibration? What are simple examples of it?
Q. 2 What are the analogous concepts of these two in category of modules or rings or something in algebra?