Factorization homology of enriched $\infty$-categories

David Ayala, Aaron Mazel-Gee, Nick Rozenblyum

Published 2017-10-17Version 1

For an arbitrary symmetric monoidal $\infty$-category $V$, we define the factorization homology of $V$-enriched $\infty$-categories over (possibly stratified) 1-manifolds and study its basic properties. In the case that $V$ is \textit{cartesian} symmetric monoidal, by considering the circle and its self-covering maps we obtain a notion of \textit{unstable topological cyclic homology}, which we endow with an \textit{unstable cyclotomic trace map}. As we show in \cite{AMR-trace}, these induce their stable counterparts through linearization (in the sense of Goodwillie calculus).