The right cancellation property for certain classes of dendroidal anodynes

TL;DR

This paper extends the right cancellation property of dendroidal inner anodynes to normal monomorphisms and uses this to construct symmetric monoidal $$-categories from dendroidal $$-operads, generalizing known operad envelopes.

Contribution

It generalizes the right cancellation property to dendroidal sets and introduces a method to construct symmetric monoidal $$-categories from dendroidal $$-operads.

Findings

Established the right cancellation property for dendroidal inner anodynes.

Provided a construction for symmetric monoidal $$-categories from dendroidal $$-operads.

Extended previous results to a broader categorical context.

Abstract

We generalize a previous result of Stevenson to the category of dendroidal sets, yielding the right cancellation property of dendroidal inner anodynes within the class of normal monomorphisms. As an application of this property, we show how to construct a symmetric monoidal $\infty$-category $\mathsf{Env}(X)^\otimes$ from a dendroidal $\infty$-operad $X$, in a way that generalizes the symmetric monoidal envelope of a coloured operad.