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Enriched ∞-categories via non-symmetric ∞-operads

- David Gepner, R. Haugseng
- Mathematics
- 11 December 2013

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, if… Expand

Iterated spans and classical topological field theories

- R. Haugseng
- Mathematics
- 2 September 2014

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 Cobordism… Expand

Lax colimits and free fibrations in ∞-categories

- David Gepner, R. Haugseng, T. Nikolaus
- Mathematics
- 2017

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, of… Expand

The higher Morita category of n–algebras

- R. Haugseng
- Mathematics
- 29 December 2014

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

- Hongyi Chu, R. Haugseng
- Mathematics
- Advances in Mathematics
- 9 July 2019

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 factorization… Expand

∞-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

- R. Haugseng
- Mathematics
- 13 December 2013

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 the… Expand

The Becker-Gottlieb Transfer Is Functorial

- R. Haugseng
- Mathematics
- 23 October 2013

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 contravariantly… Expand

Bimodules and natural transformations for enriched $\infty$-categories

- R. Haugseng
- Mathematics
- 24 June 2015

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 of… Expand

Linear Batalin–Vilkovisky quantization as a functor of $$\infty $$∞-categories

- Owen Gwilliam, R. Haugseng
- Mathematics
- 3 August 2016

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, we… Expand

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