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I had trouble working with general limits, so I rewrote the code to closer resemble the version in UniMath which I think is very nice to work with.
A cone is now a separate record and not defined in terms of natural transformations, this made it possible for me to prove that Set is complete using copatterns (this seems to have been a problem before...). The price to pay is that I have to prove some lemmas by hand (like
isSetCone
).I also added a definition of what it means for a functor to preserve a limit (of some particular shape).