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We prove a variety results on tensor product factorizations of finite dimensional Hopf algebras (more generally Hopf algebras satisfying chain conditions in suitable braided categories). The results are analogs of well-known results on…

Rings and Algebras · Mathematics 2016-02-24 Marc Keilberg , Peter Schauenburg

Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers-Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under…

Logic · Mathematics 2018-02-26 Saskia Chambille , Pablo Cubides Kovacsics , Eva Leenknegt

We define a symmetric monoidal category modelling fuzzy concepts and fuzzy conceptual reasoning within G\"ardenfors' framework of conceptual (convex) spaces. We propose log-concave functions as models of fuzzy concepts, showing that these…

Category Theory · Mathematics 2022-11-04 Sean Tull

We introduce a category Prob of probability spaces whose objects are all probability spaces and arrows are corresponding to measurable functions satisfying an absolutely continuous requirement. We can consider a Prob-arrow as an evolving…

Probability · Mathematics 2018-10-25 Takanori Adachi , Yoshihiro Ryu

In this paper (propositional) probability logic ($PL$) is investigated from model theoretic point of view. First of all, the ultraproduct construction is adapted for $\sigma$-additive probability models, and subsequently when this class of…

Logic · Mathematics 2018-10-18 Massoud Pourmahdian , Reihane Zoghifard

We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical Lipschitzian and H\"olderian error bounds and includes…

Optimization and Control · Mathematics 2023-10-20 Tianxiang Liu , Bruno F. Lourenço

Concurrency and probability are both much studied extensions of sequential computation. Within concurrency theory, there is a broad divide between interleaving models and logics, which model concurrency by non-determinism, and `truly…

Formal Languages and Automata Theory · Computer Science 2020-12-21 Nargess Ghahremani , Julian Bradfield

For a root system R, a field K and a "choice of coefficients in K" we define a category of graded spaces with operators and study some of its properties. Then we assume that the coefficients are given by quantum binomials. We use basic…

Representation Theory · Mathematics 2023-11-16 Peter Fiebig

Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations}. A logic for convergent infinite computations is…

Logic in Computer Science · Computer Science 2007-05-23 Wei Li , Shilong Ma , Yuefei Sui , Ke Xu

We recall P. Balmer's definition of tensor triangular Chow group for a tensor triangulated category $\mathcal{K}$ and explore some of its properties. We give a proof that for a suitably nice scheme $X$ it recovers the usual notion of Chow…

Algebraic Geometry · Mathematics 2015-10-02 Sebastian Klein

The commutative Hopf monoid of set compositions is a fundamental Hopf monoid internal to vector species, having undecorated bosonic Fock space the combinatorial Hopf algebra of quasisymmetric functions. We construct a geometric realization…

Combinatorics · Mathematics 2021-04-16 William Norledge , Adrian Ocneanu

On a smooth projective threefold, we construct an essentially surjective functor $\mathcal{F}$ from a category of two-term complexes to a category of quotients of coherent sheaves, and describe the fibers of this functor. Under a coprime…

Algebraic Geometry · Mathematics 2023-02-22 Jason Lo

This paper begins by noting that, in a 1969 paper in the Transactions, M.C.McCord introduced a construction that can be interpreted as a model for the categorical tensor product of a based space and a topological abelian group. This can be…

Algebraic Topology · Mathematics 2007-05-23 Nicholas J. Kuhn

Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…

Algebraic Topology · Mathematics 2020-12-03 Karthik Boyareddygari

Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…

Logic in Computer Science · Computer Science 2024-02-05 Junyoung Jang , Sophia Roshal , Frank Pfenning , Brigitte Pientka

We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…

Numerical Analysis · Mathematics 2016-07-21 Michael Griebel , Peter Oswald

We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…

Number Theory · Mathematics 2018-10-05 Martin Raum

Pomset logic introduced by Retor\'e is an extension of linear logic with a self-dual noncommutative connective. The logic is defined by means of proof-nets, rather than a sequent calculus. Later a deep inference system BV was developed with…

Logic in Computer Science · Computer Science 2023-06-22 Sergey Slavnov

One may formulate the dependent product types of Martin-L\"of type theory either in terms of abstraction and application operators like those for the lambda-calculus; or in terms of introduction and elimination rules like those for the…

Logic · Mathematics 2011-10-17 Richard Garner

Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…

Numerical Analysis · Mathematics 2018-06-19 Hermann G. Matthies , Roger Ohayon