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19 votes
2 answers
1k views

What are "fibration/cofibration" in type theory and what are their intuitions?

I keep seeing these phrasing in some proof assistants/elaborators and their issues/internal discussions (e.g. Github search results in cooltt), that seems not that related to the actual proofs/...
Anqur's user avatar
  • 301
27 votes
2 answers
879 views

What is Artin gluing, and how is it useful in proving meta-theoretic properties?

I came across this notion in several places, especially in recent papers that establish important meta-theoretic properties of type theories like CuTT. The entry in nLab focuses on the geometric ...
Trebor's user avatar
  • 4,025