For \(n \geq -1\), we say that a morphism of \(\infty\)-operads is \(n\)-surjective if it is surjective-on-objects on \(\infty\)-categories of colors and multi-homwise \((n-1)\)-connected and we say that it is \(n\)-faithful if it is multi-homwise \((n-1)\)-truncated. We extend this to the case that \(n = -2\) by declaring that every morphism of \(\infty\)-operads is \((-2)\)-surjective, and that a morphism of \(\infty\)-operads is \((-2)\)-faithful if and only if it is an equivalence.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2