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.