Scheimbauer’s factorization-algebra comparison conjecture

Let C\mathcal{C} be a nice \use@mathgroup\M@U\symAMSbEn\use@mathgroup \M@U \symAMSb{E}_{n}-monoidal \infty-category. Let AlgnFA(C)\mathfrak{Alg}_{n}^{\textup{FA}}(\mathcal{C}) denote Scheimbauer’s (,n+1)(\infty,n+1)-category of \use@mathgroup\M@U\symAMSbEn\use@mathgroup \M@U \symAMSb{E}_{n}-algebras in C\mathcal{C} defined using factorization algebras, and let CI/\mathcal{C}_{I/} be the relevant pointed slice category. Factorization-algebra comparison conjecture. There is an equivalence

AlgnFA(C)Algn(CI/).\mathfrak{Alg}_{n}^{\textup{FA}}(\mathcal{C})\simeq\mathfrak{Alg}_{n}(\mathcal{C}_{I/}).

This comparison would identify Scheimbauer’s pointed bimodule construction with the unpointed construction studied in the paper. The source presents it as an expectation for nice \use@mathgroup\M@U\symAMSbEn\use@mathgroup \M@U \symAMSb{E}_{n}-monoidal infinity-categories and gives no resolution.

Sources & referencesView supporting material

Primary source

Rune Haugseng, “The higher Morita category of E_n-algebras”, arXiv:1412.8459 (2020).

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