The topology explanation is about what I had in mind for motivation. I think to appreciate cohomology, I need appreciate what problems in homology it makes easy

The topology explanation is about what I had in mind for motivation. I think to appreciate cohomology, I need appreciate what problems in homology it makes easy to solve. To appreciate that I need have the vocabulary of algebraic topology. One way to maybe then to describe homology is it gives you way to take about shapes and surfaces in the language of algebra.