| Below I consider a notion of orthogonality with respect to cones, | generalising that of orthogonality with respect to maps and the sheaf | condition for a cover in a Grothendieck topology: | | 1. We say that an object K is orthogonal to a cone D --> C | whenever for every cone D --> K there exists a unique | C --> K such that (D --> C --> K) = (D --> K). I've come across examples of the above in stable homotopy theory, except that uniqueness of the map C --> K doesn't hold in general. (In general one only gets these weakened versions of colimits in the homotopy category, if one gets anything at all.) It seemed to me to be unnatural, but now I'm happy to find that someone else has come across these partial colimits. Could you pass on any references you know, or any that people send to you? Thanks, Dan