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Enriched ∞-categories via non-symmetric ∞-operads
Abstract We set up a general theory of weak or homotopy-coherent enrichment in an arbitrary monoidal ∞-category. Our theory of enriched ∞-categories has many desirable properties; for instance, ifExpand
Iterated spans and classical topological field theories
We construct higher categories of iterated spans, possibly equipped with extra structure in the form of higher-categorical local systems, and classify their fully dualizable objects. By the CobordismExpand
Lax colimits and free fibrations in ∞-categories
We define and discuss lax and weighted colimits of diagrams in ∞-categories and show that the coCartesian fibration corresponding to a functor is given by its lax colimit. A key ingredient, ofExpand
The higher Morita category of n–algebras
We introduce simple models for associative algebras and bimodules in the context of non-symmetric $\infty$-operads, and use these to construct an $(\infty,2)$-category of associative algebras,Expand
Homotopy-coherent algebra via Segal conditions
Many homotopy-coherent algebraic structures can be described by Segal-type limit conditions determined by an "algebraic pattern", by which we mean an $\infty$-category equipped with a factorizationExpand
∞-Operads as Analytic Monads
The aim is to study the paper “∞-operads as analytic monads” by David Gepner, Rune Haugseng, and Joachim Kock.
Rectification of enriched infinity-categories
We prove a rectification theorem for enriched infinity-categories: If V is a nice monoidal model category, we show that the homotopy theory of infinity-categories enriched in V is equivalent to theExpand
The Becker-Gottlieb Transfer Is Functorial
The Becker-Gottlieb transfer gives a wrong-way map on suspension spectra for maps of spaces whose homotopy fibres are retracts of finite complexes. We prove that this construction is contravariantlyExpand
Bimodules and natural transformations for enriched $\infty$-categories
We introduce a notion of bimodule in the setting of enriched $\infty$-categories, and use this to construct a double $\infty$-category of enriched $\infty$-categories where the two kinds ofExpand
Linear Batalin–Vilkovisky quantization as a functor of $$\infty $$∞-categories
We study linear Batalin–Vilkovisky (BV) quantization, which is a derived and shifted version of the Weyl quantization of symplectic vector spaces. Using a variety of homotopical machinery, weExpand