Proves an oriented Street-Roberts conjecture by presenting (∞,∞)-categories as sheaves on families of oriented polytopes, generalizing Campion's work.
The Gray tensor product of(∞, n)-categories
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
abstract
In this note, we leverage the author's pasting theorem for $(\infty,n)$-categories to construct new models of $(\infty,n)$-categories for all $n \leq \infty$, as presheaves on certain categories of computads. Among these new models are some which facilitate a construction of the Gray tensor product of $(\infty,n)$-categories Day convolution and reflection, which we carry out here. After constructing this Gray tensor product of $(\infty,n)$-categories, we characterize it via several model-independent universal properties.
fields
math.AT 4representative 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.
Defines categorical homology via an Eilenberg-Steenrod analogue, proves a Dold-Kan correspondence using the Street nerve, and derives a Dold-Thom theorem for multiplicative structure and globe computations.
citing papers explorer
-
An Oriented Street--Roberts Conjecture
Proves an oriented Street-Roberts conjecture by presenting (∞,∞)-categories as sheaves on families of oriented polytopes, generalizing Campion's work.
-
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.
-
Homology of higher categories
Defines categorical homology via an Eilenberg-Steenrod analogue, proves a Dold-Kan correspondence using the Street nerve, and derives a Dold-Thom theorem for multiplicative structure and globe computations.
- Higher Semiadditive Character Theory