We define a reduced ∞-operad P to be d -connected if the spaces P(n) of n-ary operations are d -connected for all n ≥ 0. Let P and Q be two reduced ∞-operads. We prove that if P is d1 -connected and Q is d2-connected, then their Boardman- Vogt tensor product (Formula Presented.) is (d1+d2+2)-connected. We consider this to be a natural ∞-categorical generalization of the classical Eckmann-Hilton argument.
- Eckmann–Hilton argument
- Infinity operads
All Science Journal Classification (ASJC) codes
- Geometry and Topology