What question did this study set out to answer?

The central aim is to explore the universal property of the little cubes operad variations and their relationships with ∞-operads.

February 8, 20260 citations

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Universal properties of variations of the little cubes operads

KAK. (Kensuke) Arakawa

Key Points

The central aim is to explore the universal property of the little cubes operad variations and their relationships with ∞-operads.
Defined a version EB of the little cubes operad based on Lurie's construction.
Showed the equivalence between operad maps and Top(n)-equivariant maps.
Constructed an explicit diagram representing EB as a colimit of En parametrized by B.
Established the universal property of EB concerning ∞-operads.
Demonstrated EB as a colimit, enhancing understanding of operad maps.
Confirmed that locally constant factorization algebras satisfy descent, reaffirming a theorem by Matsuoka.

Abstract

Given a map B → B Top(n) of spaces, one can define a version EB of the little cubes operad, whose construction is due to Lurie. We show that EB enjoys the universal property that, for every ∞-operad O, an operad map EB → O is equivalent to a Top(n)- equivariant map B ×B Top(n) E Top(n) → Map(En,O). This gives us an explicit diagram exhibiting EB as a colimit of En parametrized by B. It also shows that locally constant factorization algebras satisfy descent, reproving a recent theorem of Matsuoka.

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K. (Kensuke) Arakawa (Wed,) studied this question.

synapsesocial.com/papers/698828ab0fc35cd7a88485e8 https://doi.org/https://doi.org/10.17879/11958513737

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