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These laws of identifications have become quite subtle. While it has been clear for a long time that it is good mathematical practice to identify\n            <jats:italic>isomorphic<\/jats:italic>\n            algebraic structures [11], or at least to use only notions and facts about algebraic structures that are invariant under isomorphisms, category theory extends this to the notion of\n            <jats:italic>categorical<\/jats:italic>\n            <jats:italic>equivalences<\/jats:italic>\n            <jats:sup>1<\/jats:sup>\n            , which themselves have been generalized to higher forms of equivalences [25]. Voevodsky noticed that, by extending some versions of dependent type theory with one further axiom - the\n            <jats:italic>univalence<\/jats:italic>\n            <jats:italic>axiom<\/jats:italic>\n            - one obtains a formal system in which all notions and operations are automatically invariant under isomorphisms and even under higher notions of equivalence.\n          <\/jats:p>","DOI":"10.1145\/3242953.3242962","type":"journal-article","created":{"date-parts":[[2020,4,4]],"date-time":"2020-04-04T09:28:34Z","timestamp":1585992514000},"page":"54-65","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["A survey of constructive presheaf models of univalence"],"prefix":"10.1145","volume":"5","author":[{"given":"Thierry","family":"Coquand","sequence":"first","affiliation":[{"name":"University of G\u00f6teborg"}]}],"member":"320","published-online":{"date-parts":[[2018,7,26]]},"reference":[{"key":"e_1_2_1_1_1","series-title":"Lecture Notes in Comput. 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