arXiv subjects

Rose Kudzman-Blais

Publications and source records attributed to Rose Kudzman-Blais.

4 recordsLinked to original sources

arXiv2026

Linearly Distributive Fox Theorem

Linearly distributive categories (LDC), introduced by Cockett and Seely to model multiplicative linear logic, are categories equipped with two monoidal structures that interact via linear distributivities. A seminal result in monoidal category theory is the Fox theorem, which characterizes cartesian categories as symmetric monoidal categories whose objects are equipped with canonical comonoid structures. The aim of this work is to extend the Fox theorem to LDCs and characterize the subclass of cartesian linearly distributive categories (CLDC). To do so, we introduce medial linearly distributive categories (MLDC), medial linear functors, and medial linear transformations. The former are LDCs which respect the logical medial rule, appearing frequently in deep inference, or alternatively are the appropriate structure at the intersection of LDCs and duoidal categories.

math.CT↗

arXiv2026

Cartesian Linearly Distributive Categories: Revisited

Linearly distributive categories (LDC) were introduced by Cockett and Seely to provide alternative categorical semantics for multiplicative linear logic. In contrast to Barr's $*$-autonomous categories, LDCs take multiplicative conjunction and disjunction as primitive notions. Thus, a LDC is a category with two monoidal products that interact via linear distributors. A cartesian linearly distributive category (CLDC) is a LDC whose two monoidal products coincide with categorical products and coproducts. Initially, it was believed that CLDCs and distributive categories would coincide, but this was later found not to be the case. Consequently, the study of CLDCs was not pursued further at the time. With recent developments for and applications of LDCs, there has been renewed interest in CLDCs. This paper revisits CLDCs, demonstrating strong structural properties they all satisfy and investigating two key classes of examples: posetal distributive categories and semi-additive categories. Additionally, a previously assumed class of CLDCs, the Kleisli categories of exception monads of distributive categories, is re-examined and it is showed that they are not, in fact, CLDCs.

math.CT↗

arXiv2026

Constructing linear bicategories

Linearly distributive categories were introduced to model the tensor/par fragment of linear logic, without resorting to the use of negation. Linear bicategories are the bicategorical version of linearly distributive categories. Essentially, a linear bicategory has two forms of composition, each determining the structure of a bicategory, and the two compositions are related by a linear distribution. The main goal of this paper is to demonstrate that there are many examples of linear bicategories, which are obtained by considering quantales and quantaloids. It is standard in the field of monoidal topology that the category of quantale-valued relations is a bicategory. Here we begin by showing that a quantale is Girard if and only if the corresponding bicategory is a Girard quantaloid, which is an example of linear bicategory. The tropical and arctic semiring structures fit together into a Girard quantale, so this construction is likely to have multiple applications. More generally, we define LD-quantales, which are sup-lattices with two quantale structures related by a linear distribution, and their bicategorical analogue, linear quantaloids. We show that Q-Rel is a linear quantaloid if and only if Q is an LD-quantale. We then consider several standard constructions from enriched bicategory theory, and show that these lift to the linear quantaloid setting and produce new examples of linear bicategories. In particular, we consider linear Q-categories, matrices in Q and linear monads in Q, where Q is a linear quantaloid. We develop non-locally posetal examples as well, Quant, the bicategory of quantales, modules and module homomorphisms, and Qtld, the bicategory of quantaloids, modules and module homomorphisms. These turn out to be cyclic *-autonomous bicategories, which are in essence a closed version of linear bicategories.

math.CT↗

arXiv2019

Combined collider constraints on neutralinos and charginos

Searches for supersymmetric electroweakinos have entered a crucial phase, as the integrated luminosity of the Large Hadron Collider is now high enough to compensate for their weak production cross-sections. Working in a framework where the neutralinos and charginos are the only light sparticles in the Minimal Supersymmetric Standard Model, we use gambit to perform a detailed likelihood analysis of the electroweakino sector. We focus on the impacts of recent ATLAS and CMS searches with 36 fb$^{-1}$ of 13 TeV proton-proton collision data. We also include constraints from LEP and invisible decays of the $Z$ and Higgs bosons. Under the background-only hypothesis, we show that current LHC searches do not robustly exclude any range of neutralino or chargino masses. However, a pattern of excesses in several LHC analyses points towards a possible signal, with neutralino masses of $(m_{\tildeχ_1^0}, m_{\tildeχ_2^0}, m_{\tildeχ_3^0}, m_{\tildeχ_4^0})$ = (8-155, 103-260, 130-473, 219-502) GeV and chargino masses of $(m_{\tildeχ_1^{\pm}}, m_{\tildeχ_2^{\pm}})$ = (104-259, 224-507) GeV at the 95% confidence level. The lightest neutralino is mostly bino, with a possible modest Higgsino or wino component. We find that this excess has a combined local significance of $3.3σ$, subject to a number of cautions. If one includes LHC searches for charginos and neutralinos conducted with 8 TeV proton-proton collision data, the local significance is lowered to 2.9$σ$. We briefly consider the implications for dark matter, finding that the correct relic density can be obtained through the Higgs-funnel and $Z$-funnel mechanisms, even assuming that all other sparticles are decoupled. All samples, gambit input files and best-fit models from this study are available on Zenodo.

hep-ph↗