Two-variable fibrations, factorisation systems and $\infty $ -categories of spans

Abstract

We prove a universal property for $\infty $ -categories of spans in the generality of Barwick’s adequate triples, explicitly describe the cocartesian fibration corresponding to the span functor, and show that the latter restricts to a self-equivalence on the class of orthogonal adequate triples, which we introduce for this purpose.

Keywords

• 18N70
• 18N60
• 18N65