>Then there are categories like \\(\mathbf{FinVect}\\), the category of finite-dimensional vector spaces and linear maps, that are equivalent to their own opposite. These are neither like \\(\mathbf{Set}\\) nor like \\(\mathbf{Set}^{\text{op}}\\), but somehow poised right in between.

WOW. I knew vector spaces are beautiful mathematical objects but this is yet again mind blowing. Sounds like they are kind of like a hologram of adjunctions.