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The notion of retrocell in a double category with companions is introduced and its basic properties established. Explicit descriptions in some of the usual double categories are given. Monads in a double category provide an important…

Category Theory · Mathematics 2023-06-19 Robert Paré

We produce a fully faithful functor from finite type nilpotent spaces to cosimplicial binomial rings, thus giving an algebraic model of integral homotopy types. As an application, we construct an integral version of the…

Algebraic Topology · Mathematics 2025-03-25 Geoffroy Horel

We study a 2-functor that assigns to a bimodule category over a finite k-linear tensor category a k-linear abelian category. This 2-functor can be regarded as a category-valued trace for 1-morphisms in the tricategory of finite tensor…

Category Theory · Mathematics 2016-01-20 Jurgen Fuchs , Gregor Schaumann , Christoph Schweigert

The proof, but not the statement, of Proposition 18.2 contained an error which is repaired in this version. See Remark 18.3 in this version. No other changes. We extend Greenberg's original construction to arbitrary (in particular,…

Number Theory · Mathematics 2022-02-22 Alessandra Bertapelle , Cristian D. Gonzalez-Aviles

We introduce a notion of bimodule in the setting of enriched $\infty$-categories, and use this to construct a double $\infty$-category of enriched $\infty$-categories where the two kinds of 1-morphisms are functors and bimodules. We then…

Algebraic Topology · Mathematics 2020-11-03 Rune Haugseng

We introduce the notion of numerical functors to generalise Eilenberg & MacLane's polynomial functors to modules over a binomial base ring. After shewing how these functors are encoded by modules over a certain ring, we record a precise…

Representation Theory · Mathematics 2015-09-24 Qimh Richey Xantcha

Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…

General Relativity and Quantum Cosmology · Physics 2018-10-18 Giampiero Esposito

Let G be a finite group. We systematically exploit general homological methods in order to reduce the computation of G-equivariant KK-theory to topological equivariant K-theory. The key observation is that the functor assigning to a…

Operator Algebras · Mathematics 2016-05-11 Ivo Dell'Ambrogio

In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…

High Energy Physics - Theory · Physics 2011-07-19 D. G. C. McKeon , A. Rebhan

A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of…

Mathematical Physics · Physics 2015-05-14 John T. Conway , Howard S. Cohl

We develop the theory of Mackey profunctors, a version of Mackey functors for profinite groups.

K-Theory and Homology · Mathematics 2022-09-20 D. Kaledin

We show that induction of covariant representations for C*-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of…

Operator Algebras · Mathematics 2007-05-23 Siegfried Echterhoff , S. Kaliszewski , John Quigg , Iain Raeburn

In this paper we develop the theory of topological categories over a base category, that is, a theory of topological functors. Our notion of topological functor is similar to (but not the same) the existing notions in the literature (see…

Category Theory · Mathematics 2007-05-23 Eduardo J. Dubuc , Luis Español

This is the second paper in a series. In part I we developed deformation theory of objects in homotopy and derived categories of DG categories. Here we extend these (derived) deformation functors to an appropriate bicategory of artinian DG…

Algebraic Geometry · Mathematics 2018-08-13 Alexander I. Efimov , Valery A. Lunts , Dmitri O. Orlov

Octonions are introduced through some spin representations. The groups $G_2$, $F_4$ and the $E$ series appear in a natural manner; one way to understand octonions is as the "second coming" of the reals, but with the spinors instead of…

Mathematical Physics · Physics 2007-05-23 Luis J. Boya

We study the notion of a "differential 2-rig", a category R with coproducts and a monoidal structure distributing over them, also equipped with an endofunctor D : R -> R that satisfies a categorified analogue of the Leibniz rule. This is…

Category Theory · Mathematics 2023-08-01 Fosco Loregian , Todd Trimble

Hypergeometric functions over finite fields were introduced by Greene in the 1980s as a finite field analogue of classical hypergeometric series. These functions, and their generalizations, naturally lend themselves to, and have been widely…

Number Theory · Mathematics 2023-08-04 Madeline Locus Dawsey , Dermot McCarthy

This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give…

Category Theory · Mathematics 2013-09-26 Rina Anno

For all subgroups $H$ of a cyclic $p$-group $G$ we define norm functors that build a $G$-Mackey functor from an $H$-Mackey functor. We give an explicit construction of these functors in terms of generators and relations based solely on the…

Algebraic Topology · Mathematics 2019-08-02 Michael A. Hill , Kristen Mazur

Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…

Programming Languages · Computer Science 2015-02-05 Mauro Jaskelioff , Russell O'Connor