Hard Facts

Soon to figure out how to write theorem environments in markdown. Until then…

Theorem : Let \(\mathbf{FMan}\) be the category whose objects are simply connected smooth manifolds with flat connection, and whose arrows are diffeomorphisms that preserve the connection. Let \(\mathbf{Aff}\) be the category of affine spaces and affine maps. Then \(\mathbf{FlMan}\) and \(\mathbf{Aff}\) are equivalent categories.