Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
@TimCampion Thanks a lot. At first I was thinking to use the category is left proper and try to use pushout of weak equivalence of cofibration is weak equivalence. I miss the map itself is acyclic cofibration.
@TimCampion Thank you for adding the tag. Using theorem 3.3 will make things harder for me as I lack those kind of knowledge. But I quite agree with your second comment and this fully resolve my question. Thanks.
