Product preserving functors of infinite dimensional manifolds

Product preserving bundle functors on multifibered and multifoliate manifolds

We show that the set of the equivalence classes of multifoliate structures is in one-to-one correspondence with the set of equivalence classes of finite complete projective systems of vector space epimorphisms. After that we give the complete description of all product preserving bundle functors on the categories of multifibered and multifoliate manifolds.

diffeological 空间上无穷多个切 functor

Infinitely Many Tangent Functors on Diffeological Spaces

本文研究 diffeological 空间上的切 functor，构建了无穷多个非同构的切 functor，并表明在非光滑流形外，切 functor 的选择并不唯一。

On the infinite dimensional hidden symmetries. II. $q_R$-conformal modular functor

The article is devoted to the $q_R$-conformal modular functors, which being ``deformations'' of the conformal modular functor (the projective representation of the category $Train(Diff_+(S^1))$, the train of the group $Diff_+(S^1)$ of all orientation preserving diffeomorphisms of a circle) in the class of all projective modular functors (the projective representations of the category $Train(PSL(2,R))$, the train of the projective group $PSL(2,R)$), may be regarded as its ``Berezin quantizations''.

Infinite-Dimensional Supermanifolds via Multilinear Bundles

In this paper, we provide an accessible introduction to the theory of locally convex supermanifolds in the categorical approach. In this setting, a supermanifold is a functor $\mathcal{M}\colon\mathbf{Gr}\to\mathbf{Man}$ from the category of Grassmann algebras to the category of locally convex manifolds that has certain local models, forming something akin to an atlas. We give a mostly self-contained, concrete definition of supermanifolds along these lines, closing several gaps in the literature on the way. If $Λ_n\in\mathbf{Gr}$ is the Grassmann algebra with $n$ generators, we show that $\mat…

Relative homological algebra, equivariant de Rham theory, and Koszul duality

Let G be a general (not necessarily finite dimensional compact) Lie group, let g be its Lie algebra, let Cg be the cone on g in the category of differential graded Lie algebras, and consider the functor which assigns to a chain complex V the V-valued total de Rham complex of G. We describe the G-equivariant de Rham cohomology in terms of a suitable relative differential graded Ext, defined on the appropriate category of (G,Cg)-modules. The meaning of "relative" is made precise via the dual standard construction associated with the monad involving the aforementioned functor and the associated f…

函子场论中自由费米子的手征反常

The Chiral Anomaly of the Free Fermion in Functorial Field Theory

本研究针对函子场论框架下自由费米子的手征反常问题，构造了将流形映射为无限维克利福德代数、配边映射为双模的函子形式的反常理论，解释了狄拉克算符行列式对应复直线元素的扭曲特性。