A V-enriched ∞-operad is equivalent to a presentably symmetric monoidal V-module category generated by a ⊗-atomic marking of its colors.
The Algebra of Categorical Spectra
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
Categorical spectra are spectrum objects in pointed $(\infty,\infty)$-categories: sequences $(X_n)$ equipped with equivalences $X_n\simeq \Omega X_{n+1}$. This thesis develops foundations for categorical spectra and constructs their tensor product, the stabilized analogue of the lax Gray tensor product of $(\infty,\infty)$-categories. We use this tensor product to study stability phenomena, expressed as the coincidence of certain finite weighted colimits and limits. As an application, we give a precise categorical derivation of the cobordism hypothesis with singularities from the ordinary cobordism hypothesis, making rigorous a sketch of Lurie.
fields
math.AT 2years
2026 2representative citing papers
Inverting endomorphism categories produces a stable homotopy theory of higher categories in which categorical spectra classify homology theories via a categorical Brown representability theorem.
citing papers explorer
-
Enriched $\infty$-operads as marked algebras
A V-enriched ∞-operad is equivalent to a presentably symmetric monoidal V-module category generated by a ⊗-atomic marking of its colors.
-
Stable homotopy theory of higher categories
Inverting endomorphism categories produces a stable homotopy theory of higher categories in which categorical spectra classify homology theories via a categorical Brown representability theorem.