Factorization homology I: higher categories

Understand

We construct a pairing, which we call factorization homology, between framed manifolds and higher categories.

• The essential geometric notion is that of a vari-framing of a stratified manifold, which is a framing on each stratum together with a coherent system of compatibilities of framings along links between strata.
• Our main result constructs labeling systems on disk-stratified vari-framed $n$-manifolds from $(\infty,n)$-categories.
• These $(\infty,n)$-categories, in contrast with the literature to date, are not required to have adjoints.