Related papers: The cube and the Burnside category

In this paper we study conjugacy classes for pivotal fusion categories. In particular we prove a Burnside type formula for the structure constants concerning the product of two conjugacy class sums of a such fusion category. For a braided…

We provide a complete characterization of the equivariant commutative ring structures of all the factors in the idempotent splitting of the G-equivariant sphere spectrum, including their Hill-Hopkins-Ravenel norms, where G is any finite…

We study the homotopy theory of a certain type of diagram categories whose vertices are in variable categories with a functorial path, leading to a good calculation of the homotopy category in terms of cofibrant objects. The theory is…

We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…

In this paper we study a model structure on a category of schemes with a group action and the resulting unstable and stable equivariant motivic homotopy theories. The new model structure introduced here samples a comparison to the one by…

We exhibit a set of generating relations for the modular invariant ring of a vector and a covector for the two-dimensional general linear group over a finite field.

We define the projective stable category of a coherent scheme. It is the homotopy category of an abelian model structure on the category of unbounded chain complexes of quasi-coherent sheaves. We study the cofibrant objects of this model…

A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets,…

Higson proved that every homotopy invariant, stable and split exact functor from the category of $C^*$-algebras to an additive category factors through Kasparov's $KK$-theory. By adapting a group equivariant generalization of this result by…

The combinatorial interpretation of the persistence diagram as a M\"obius inversion was recently shown to be functorial. We employ this discovery to recast the Persistent Homology Transform of a geometric complex as a representation of a…

This is the second paper in a series on enumerative invariants counting self-dual objects in self-dual categories, and is a sequal to (arXiv:2302.00038). Ordinary enumerative invariants in abelian categories can be seen as invariants for…

We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories. The…

This article tackles categorical coherence within a two-dimensional generalization of Lawvere's functorial semantics. 2-theories, a syntactical way of describing categories with structure, are presented. From the perspective here afforded,…

In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus $\tau$ and its conjugate, $\bar\tau$. We point out that certain combinations of…

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…

We show that the category of corings over a fixed base ring with local units is equivalent to the category of comonads in (right) unital modules whose underlying functors preserve inductive limits. Changing base rings, we prove a…

We prove that if two knots are concordant, their involutive knot Floer complexes satisfy a certain type of stable equivalence.

In this paper we introduce two theories of finite type invariants for framed links with fixed linking matrix. We show that these thepries are related to the theory of Vassiliev invariants of framed links. We also study the corresponding…

We show that the covariant derivative of a spinor for a general affine connection, not restricted to be metric compatible, is given by the Fock-Ivanenko coefficients with the antisymmetric part of the Lorentz connection. The projective…

We define numerical link-homotopy invariants of link maps of any number of components, which naturally generalize the Kirk invariant. The Kirk invariant is a link-homotopy invariant of 2-component link maps given by linking numbers of loops…