Enriched homotopy-coherent structures

We introduce a general notion of enrichment for homotopy-coherent algebraic structures described by Segal conditions, using the framework of "algebraic patterns" developed in our previous work. This recovers several known examples of enriched structures, including enriched \(\infty\)-categories, enriched \(\infty\)-operads, and enriched \(\infty\)-properads. As new examples we discuss enriched modular \(\infty\)-operads, enriched \(n\)-fold \(\infty\)-categories, and a non-iterative definition of enriched \((\infty,n)\)-categories.