I needed to spell out somewhere a very basic expositional example of what goes wrong in $\mathcal{K}(\mathcal{A})$ that is rectified in the derived category such that the example roughly motivates the idea of projective resolutions. I ended up putting it here into a new section *Examples - Chain homotopies that ought to exist but do not*. It could probably go elsewhere just as well.

I have expanded *homotopy category of chain complexes* by adding a few basics.

In the course of this I have also touched the formatting of the following entries:

triangulated category (and all the related, such as enhanced dg-category)

Will be further working on *derived category* now.

thought we’d need an entry *homotopy category of chain complexes*