Refactor space and directed univalence - #206
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- [x] Proves lemma #192 (with brute force as opposed to the method via left anodyne maps being stable under base change by right fibrations). - [x] Proves more generally that a covariant family exponentiated by any contravariant family is covariant - [x] Updates Spaces to use this proof Also makes tr-cov-hom and related lemmas opaque to improve goal display (and maybe performance) extracted from #206
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Builds on #218 Extracted from #206 - [x] Adds directed gluing/univalence lemma for covariant families (that no longer relies on having representing object for LFib) - [x] Uses the above lemma for directed univalence for the category of spaces - [x] Extracts lemma about detecting fibrewise equivalences of covariant families so that it doesn't mention spaces --------- Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
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Towards "Space is Segal"