Bartosz Milewski on Nostr: Here's a crazy idea: Duality plays an important role in category theory. You can ...

Here's a crazy idea: Duality plays an important role in category theory. You can produce a mirror image of a category by reversing all its arrows. It's like a discrete symmetry. Can we make it into a continuous symmetry? With a parameter going from 0 (original category) to 1 (opposite category). We would fade out the original arrows and fade in the reversed ones. The intermediate state would be some kind of enriched category. We could then interpolate between limits and colimits, left and right Kan extensions, etc.