Related papers: $\mathfrak F$-categories and $\mathfrak F$-functor…

We introduce a categorical framework for the study of representations of $G_F$, where $G$ is a reductive group, and $\bF$ is a 2-dimensional local field, i.e. $F=K((t))$, where $K$ is a local field. Our main result says that the space of…

In this article we analyze the structure of $2$-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under which condition the resulting…

In this paper, we obtain new estimates on generalization of Hermite-Hadamard, Simpson and Ostrowski type inequalities for functions whose second derivatives is $\varphi$-convex via fractional integrals.

In this paper we present a new way to construct the pro-category of a category. This new model is very convenient to work with in certain situations. We present a few applications of this new model, the most important of which solves an…

We define the character of a group representation in a 2-category C. For linear C, this notion yields a Hopkins-Kuhn-Ravenel type character theory defined on pairs of commuting elements of the group. We discuss some examples and prove a…

In this paper, we continue the study of the category of functors Fquad, associated to F_2-vector spaces equipped with a nondegenerate quadratic form, initiated in two previous papers of the author. We define a filtration of the standard…

We derive the representation theory of $SU(2)$ from the expository theory of Lie groups and Lie algebras. Based on this, the mathematics of non-relativistic quantum mechanics of a spin $\frac{1}{2}$ particle are described from a…

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…

We prove general adjoint functor theorems for weakly (co)complete $n$-categories. This class of $n$-categories includes the homotopy $n$-categories of (co)complete $\infty$-categories, so these $n$-categories do not admit all small…

We construct the quadratic analogue of the boson Fock functor. While in the first order case all contractions on the 1--particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much…

We study the geometry and partial differential equations arising from the consideration of group-determinants, and representation theory. The simplest and most striking such example is undoubtedly that of the Humbert operator, associated…

We give a combinatorial description of the dg category of character sheaves on a complex reductive group $G$, extending results of [Li] for $G$ simply-connected. We also explicitly identify the parabolic induction/restriction functors.

We show that the (2-)category of categorical representations of the loop group embeds fully faithfully into the (2-)category of factorization module categories with respect to the affine Grassmannian.

The degree by which a function can be differentiated need not be restricted to integer values. Usually most of the field equations of physics are taken to be second order, curiosity asks what happens if this is only approximately the case…

Let $R$ be a commutative ring. We investigate $R$-modules which can be written as \emph{finite} sums of {\it {second}} $R$-submodules (we call them \emph{second representable}). We provide sufficient conditions for an $R$-module $M$ to be…

The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring…

We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.

In the context of infinity categories, we rethink the notion of derived functor in terms of correspondences. This is especially convenient for the description of a passage from an adjoint pair (F,G) of functors to a derived adjoint pair…

In a recent paper, Cohl and Costas-Santos derived a number of interesting multi-derivative and multi-integral relations for associated Legendre and Ferrers functions in which the orders of those functions are changed in integral steps.…

We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.