First of all I don't know much about homological algebra, and algebraic topology I just took a class using Kinsey book (Topology of Surfaces) which is undergraduate math class and I learned what is homology group and how to calculate it from a complex.
This frist defines a directed cell complex and then generate $k$-chain group from $k$-skeleton. After that considering chain complex, with boundary operation, kinsey defines homology group.
However, Munkres and Hatcher and other algebraic topology book does not follow this way. Every text I have generate $k$-chain group from Simplicial complex not, directed cell complex. (Hatcher uses $\Delta$ complex but every $Delta$ complex can be subdivided into simplical so this does not matter).
I want to know how Kinsey's process makes sense. Please Help.