Complete Segal Objects
arXiv:1805.03561
Abstract
We define complete Segal objects, which play the role of internal higher category objects. Then we study them using representable Cartesian fibrations, in particular defining adjunctions and limits of complete Segal objects. Finally we use Segal objects to define univalence in a locally Cartesian closed category that is not presentable and generalize some previous results to the non-presentable setting.
44 Pages