[cygx]

even more in geometric algebra: dF = J

You can do that using differential forms as well - using the co-differential δ, we can write a single equation (δ + d)F = J. However, from the perspective of Yang-Mills theory, that's a rather questionable approach as we're stitching together the Bianchi identity and the Yang-Mills equation for no particular reason...

[jordibc]

Cool, I didn't know that. Still, the main point of the geometric algebra version is that it's not a "stitching" exercise, but a natural operation in the algebra -- and even better, an invertible one.