Postulate components of coherent two-sided inverses for function extensionality and univalence #1119
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fredrik-bakke
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Changes the postulates for funext and univalence such that there is judgmentally only one converse map to
htpy-eqandequiv-eq. The main benefit, however, is that noweq-htpyandeq-equivwill appear with their own names in Agda interactive mode, rather than aspr1 (pr1 (funext ... ...))andpr1 (pr1 (univalence ... ...)).I leave it for potential future work to prove
is-retraction-eq-(equiv|htpy)'andcoh-eq-(equiv|htpy)'rather than postulate them, if we want this. Note that we could get away with even fewer postulates if we really wanted to (seeTypeTopology/UF.Lower-FunExt).