Univalent higher categories via complete semi-segal types - Capriotti, Paolo; Kraus, Nicolai (Association for Computing Machinery, 2018)
Category theory in homotopy type theory is intricate as categorical laws can only be stated “up to homotopy”, and thus require coherences. The established notion of a univalent category (as introduced by Ahrens et al.)solves this by considering only truncated types, roughly corresponding to an ordinary category. This fails to capture many naturally occurring structures, stemming from the fact that the naturally occurring structures in homotopy type theory are not ordinary, but rather higher categories.