Related papers: Categorical Foundations for K-Theory

In this paper we study the "holomorphic K-theory" of a projective variety, which is defined in terms of the homotopy type of spaces of holomorphic maps from the variety to Grassmannians and loop groups. This theory was introduced by Lawson,…

Generalized differential cohomology theories, in particular differential K-theory (often called "smooth K-theory"), are becoming an important tool in differential geometry and in mathematical physics. In this survey, we describe the…

We develop a categorical analogue of Clifford theory for strongly graded rings over graded fusion categories. We describe module categories over a fusion category graded by a group $G$ as induced from module categories over fusion…

Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas…

This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a…

We prove that for a large class of well-behaved cocomplete categories $\mathcal C$ the weak and strong Drinfeld centers of the monoidal category $\mathcal{E}$ of cocontinuous endofunctors of $\mathcal{C}$ coincide. This generalizes similar…

We compute K-theory for ring C*-algebras in the case of higher roots of unity and thereby completely determine the K-theory for ring C*-algebras attached to rings of integers in arbitrary number fields.

Algebraic structures such as monoids, groups, and categories can be formulated within a category using commutative diagrams. In many common categories these reduce to familiar cases. In particular, group objects in Grp are abelian groups,…

We develop the theory of a category ${\mathscr C}_A$ which is a generalisation to non-restricted ${\mathfrak g}$-modules of a category famously studied by Andersen, Jantzen and Soergel for restricted ${\mathfrak g}$-modules, where…

Connections between heaps of modules and (affine) modules over rings are explored. This leads to explicit, often constructive, descriptions of some categorical constructions and properties that are implicit in universal algebra and…

Since the time when the first optical instruments have been invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way to formalize it in mathematics is…

Consider an o-minimal structure on the real field. Let $M$ be a definable $C^r$ manifold, where $r$ is a nonnegative integer. We first demonstrate an equivalence of the category of definable $C^r$ vector bundles over $M$ with the category…

We show that every involutive Hopf monoid in a complete and finitely cocomplete symmetric monoidal category gives rise to invariants of oriented surfaces defined in terms of ribbon graphs. For every ribbon graph this yields an object in the…

We define a notion of Koszul dual of a monoid object in a monoidal biclosed model category. Our construction generalizes the classic Yoneda algebra $Ext_A(k,k)$. We apply this general construction to define the Koszul dual of a category…

Let H be a finite dimensional Hopf algebra over a field k and A an H-module algebra over k. Khovanov and Qi defined acyclic objects and quasi-isomorphisms by using null-homotopy and contractible objects. They also defined the cofibrant…

We introduce a model category of spaces based on the definable sets of an o-minimal expansion of a real closed field. As a model category, it resembles the category of topological spaces, but its underlying category is a coherent topos. We…

Let $W$ be a finite dimensional algebraic structure (e.g. an algebra) over a field $K$ of characteristic zero. We study forms of $W$ by using Deligne's Theory of symmetric monoidal categories. We construct a category $\mathcal{C}_W$, which…

We give a 3-categorical, purely formal argument explaining why on the category of Kleisli algebras for a lax monoidal monad, and dually on the category of Eilenberg-Moore algebras for an oplax monoidal monad, we always have a natural…

We develop a rigidity criterion to show that in simplicial model categories with a compatible symmetric monoidal structure, operad structures can be automatically lifted along certain maps. This is applied to obtain an unpublished result of…

We give the definition of a kind of building I for a symmetrizable Kac-Moody group over a field K endowed with a dicrete valuation and with a residue field containing C. Due to some bad properties, we call this I a hovel. Nevertheless I has…