i'm reading a paper by Valery A. Lunts, called Coherent Sheaves on Configuration Schemes. It's about extending the usual notion the
bounded derived category of coherent sheaves on a scheme to a configuration scheme, which is a collection of schemes, some of which have morphisms between them. The case mostly considered in the paper is when the morphisms are closed embedding but you can also replace them by affine morphisms. I'll try to post more when I read more from the paper, and more importantly, understand more from the paper!