Michael Barr (McGill) Derived functors using effacements Abstract: It is well known that Tor, for example, can be defined using flat resolutions instead of projective. However, the usual proof involves starting with a projective resolution which can be mapped to the flat resolution and then comparing them. I got curious about defining Tor using flat resolutions even in the absence of projective resolutions. For example in module categories in a topos, objects have flat resolutions but not usually projective resolutions. I actually explore this for a right exact functor T: A --> C, using what I call effaceable objects.