Related papers: Differential bundles as functors from free modules
The most important examples of a double vector bundle are provided by iterated tangent and cotangent functors: TTM, TT^*M, T^*TM, and T^*T^*M. We introduce the notions of the dual double vector bundle and the dual double vector bundle…
Topos theory is a category-theoretic axiomatization of set theory. Model categories are a category-theoretical framework for abstract homotopy theory. They are complete and cocomplete categories endowed with three classes of morphisms…
Let A be an algebra with a countable basis and let B be, say, a Frechet algebra that contains A as a dense subalgebra. This embedding induces a functor from the derived category of B-modules to the derived category of A-modules. In many…
In this paper, we show that the category of Mackey-complete, separated, topological convex bornological vector spaces and bornological linear maps is a differential category. Such spaces were introduced by Fr\"olicher and Kriegl, where they…
For an endofunctor $F\colon\mathcal{C}\to\mathcal{C}$ on an ($\infty$-)category $\mathcal{C}$ we define the $\infty$-category $\operatorname{Cart}(\mathcal{C},F)$ of generalized Cartier modules as the lax equalizer of $F$ and the identity.…
We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. We show that such a bundle has an underlying…
Let \(C\) be a smooth projective curve over an algebraically closed field of characteristic zero. For the moduli space \(N(r,L)\) of stable vector bundles on \(C\) of rank \(r\) with fixed determinant \(L\), we study the group of exact…
This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion…
In this paper we continue the study of triangular matrix categories $\mathbf{\Lambda}=\left[ \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix}\right]$ initiated in [21]. First, given an additive category $\mathcal{C}$…
We equip the category of vector bundles over the vertices of a locally finite $\tilde{A}_{n-1}$ building $\Delta$ with the structure of a module category over a category of type $A_{n}$ webs in positive characteristic. This module category…
Differential categories axiomatize the basics of differentiation and provide categorical models of differential linear logic. A differential category is said to have antiderivatives if a natural transformation $\mathsf{K}$, which all…
Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also constructed abstractly starting from an arbitrary almost Lie…
We characterize Kaehler manifolds with trivial logarithmic tangent bundle (with respect to a divisor D) as a class of certain compatifications of complex semi-tori.
The calculus of variations for lagrangians which are not functions on the tangent bundle, but sections certain affine bundles is developed. We follow a general approach to variational principles which admits boundary terms of variations.
The categorical formulation of the Eilenberg-Watts calculus relates, for any pair of finite categories M and N, the finite categories Fun^{le}(N,M) and Fun^{re}(N,M) of linear left or right exact functors and the Deligne product \bar N…
A Mackey type decomposition for group actions on abelian categories is described. This allows us to define new Mackey functors which associates to any subgroup the $K$-theory of the corresponding equivariantized abelian category. In the…
We define functorial isomorphisms of parallel transport along \'etale paths for a class of principal $G$-bundles on a $p$-adic curve. Here $G$ is a connected reductive algebraic group of finite presentation and the considered principal…
In [arXiv:1509.02937], the notion of a module tensor category was introduced as a braided monoidal central functor $F\colon \mathcal{V}\longrightarrow \mathcal{T}$ from a braided monoidal category $\mathcal{V}$ to a monoidal category…
In this paper, we relate Lie algebroids to Costello's version of derived geometry. For instance, we show that each Lie algebroid $L$-and the natural generalization to dg Lie algebroids-provides an (essentially unique) $L_\infty$ space. More…
We interpret ontological models for finite-dimensional quantum theory as functors from the category of finite-dimensional Hilbert spaces and bounded linear maps to the category of measurable spaces and Markov kernels. This uniformises…