Do you want to publish a course? Click here

Bimodules and natural transformations for enriched $infty$-categories

190   0   0.0 ( 0 )
 Added by Rune Haugseng
 Publication date 2015
  fields
and research's language is English
 Authors Rune Haugseng




Ask ChatGPT about the research

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 1-morphisms are functors and bimodules. We then consider a natural definition of natural transformations in this context, and show that in the underlying $(infty,2)$-category of enriched $infty$-categories with functors as 1-morphisms the 2-morphisms are given by natural transformations.



rate research

Read More

123 - Rune Haugseng 2019
Using the description of enriched $infty$-operads as associative algebras in symmetric sequences, we define algebras for enriched $infty$-operads as certain modules in symmetric sequences. For $mathbf{V}$ a nice symmetric monoidal model category, we prove that strict algebras for $Sigma$-cofibrant operads in $mathbf{V}$ are equivalent to algebras in the associated symmetric monoidal $infty$-category in this sense. We also show that $mathcal{O}$-algebras in $mathcal{V}$ can equivalently be described as morphisms of $infty$-operads from $mathcal{O}$ to endomorphism operads of (families of) objects of $mathcal{V}$.
In this paper we present background results in enriched category theory and enriched model category theory necessary for developing model categories of enriched functors suitable for doing functor calculus.
157 - Rune Haugseng 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 familiar homotopy theory of categories strictly enriched in V. It follows, for example, that infinity-categories enriched in spectra or chain complexes are equivalent to spectral categories and dg-categories. A similar method gives a comparison result for enriched Segal categories, which implies that the homotopy theories of n-categories and (infinity,n)-categories defined by iterated infinity-categorical enrichment are equivalent to those of more familia
In this paper we complete a chain of explicit Quillen equivalences between the model category for $Theta_{n+1}$-spaces and the model category of small categories enriched in $Theta_n$-spaces. The Quillen equivalences given here connect Segal category objects in $Theta_n$-spaces, complete Segal objects in $Theta_n$-spaces, and $Theta_{n+1}$-spaces.
103 - Tyler Lawson 2016
The invertibility hypothesis for a monoidal model category S asks that localizing an S-enriched category with respect to an equivalence results in an weakly equivalent enriched category. This is the most technical among the axioms for S to be an excellent model category in the sense of Lurie, who showed that the category of S-enriched categories then has a model structure with characterizable fibrant objects. We use a universal property of cubical sets, as a monoidal model category, to show that the invertibility hypothesis is consequence of the other axioms.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا