Let \(\mathcal O\) be an \(\infty\)-operad and \(k,n\geq -2\). An \(\mathcal O\)-monoidal functor \(F\colon \mathcal C\rightarrow\mathcal D\) of \(\mathcal O\)-monoidal \((\infty,k)\)-categories (i.e. a morphism of \(\mathcal O\)-algebras in the Cartesian symmetric monoidal category \(\mathrm{Cat}_{(\infty, {k})}\)) is called \(n\)-surjective/\(n\)-faithful if for every color \(X\in \underline{\mathcal O}\), the underlying functor \(F_X \colon \mathcal C_X \rightarrow\mathcal D_X\) is \(n\)-surjective/\(n\)-faithful.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2