Dear categorists, where should I look if I wanted to know more about doing cohomology via the internal language of a topos? The idea would be to do cohomology on X in the internal language of sheaves on X. Surely, this has been worked out? For example, I know I should look into the book by Moerdijk and Reyes on Synthetic Differential Geometry to see whether their treatment of deRham cohomology is (can be) expressed in the internal language of one of those smooth toposes. Perhaps there is a better reference for this? But how about other kinds of cohomology? For example, cohomology of X with coefficients coming from a sheaf of groups on X should be just "ordinary" cohomology of some sort inside Sh(X), no? Disclaimer: I know next to nothing about cohomology. Best regards, Andrej 21-Jun-2005 14:05:02 -0300,3867;000000000001-00000017