Envelopes for algebraic patterns

We generalize Lurie's construction of the symmetric monoidal envelope of an 1-operad to the setting of algebraic patterns.This envelope becomes fully faithful when sliced over the envelope of the terminal object, and we characterize its essential image.Using this, we prove a comparison result that allows us to compare analogues of 1-operads over various algebraic patterns.In particular, we show that the G-1-operads of Nardin and Shah are equivalent to "fibrous patterns" over the .2;1/-category Span.F G / of spans of finite G-sets.When G is trivial this means that Lurie's 1-operads can equivalently be defined over Span.F / instead of F .18N70; 18N60 1. Introduction 5319 2. Envelopes for factorization systems 5324 3.