Deformation Theory for (∞,n)-categories

2025/04/23 by Roman Kositsyn, Kositsyn, Roman
Mathematics · Medicine · #18N15 (Secondary) #18N65 (Primary) 18N60 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.2504.16326

openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

For an (∞,n)-category \mathscr E we define an (∞,1) category TwAr(\mathscr E) and provide an isomorphism between the stabilization of the overcategory of \mathscr E in Cat_(∞,n) and the ∞-category of spectrum-valued functors on TwAr(\mathscr E). We use this to develop the deformation theory of (∞,n)-categories and apply it to given an ∞-categorical characterization of lax-idempotent monads.

Related

• (∞,n)-categories in context
• Categorical Theory of (∞,ω)-Categories
• Formal category theory in ∞-equipments II: Lax functors, monoidality and fibrations
• A short course on ∞-categories
• On the straightening of every functor