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Dagger categories of relations: the equivalence of dilatory dagger categories and epi-regular independence categories
Matthew Di Meglio, Chris Heunen, Jean-Simon Pacaud Lemay, Paolo Perrone, Dario Stein
https://arxiv.org/abs/2508.01146

Dagger categories of relations: the equivalence of dilatory dagger categories and epi-regular independence categories
Several categories look like categories of relations, but do not fit the established theory of relations in regular categories. They include the category of surjective multivalued functions, the category of injective partial functions, the category of finite probability spaces and stochastic matrices, and the category of Hilbert spaces and linear contractions. To explain these anomalous examples, we develop a parallel theory of relations in epi-regular independence categories. Just as regular c…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Combs, Causality and Contractions in Atomic Markov Categories
Dario Stein, M\'ark Sz\'eles

Passive Vibration Isolation Characteristics of Negative Extensibility Metamaterials
Somya Ranjan Patro, Hemant Sharma, Seokgyu Yang, Jinkyu Yang
https://arxiv.org/abs/2507.00396

Passive Vibration Isolation Characteristics of Negative Extensibility Metamaterials
Negative extensibility refers to the category of mechanical metamaterials having an unusual phenomenon where the system contracts upon expansion. The dynamic analysis of such systems is crucial for exploring the vibration isolation characteristics, forming the prime focus of the present study. Inspired by the Braess paradox, the mechanical model incorporates coupled tunable nonlinear spring stiffness properties (strain hardening and softening), which alternate when a certain displacement thresh…

Local presentability and monadicity of forgetful functors for operator algebraic categories
Alexandru Chirvasitu, Ian Thompson
https://arxiv.org/abs/2507.23152 https://

Local presentability and monadicity of forgetful functors for operator algebraic categories
In recent work of Lindenhovius and Zamdzhiev, it was established that the category of complete operator spaces, with completely contractive linear maps as morphisms, is locally countably presentable. In this work, we extend their conclusion to the non-complete setting and prove that the categories of operator systems, (Archimedean) order unit spaces, and unital operator algebras are all locally countably presentable as well. This is established through an analysis of forgetful functors and the …

A Completeness Theorem for Topological Doctrines
Silvio Ghilardi, J\'er\'emie Marqu\`es
https://arxiv.org/abs/2507.20768 https://arxiv.org/pdf/2507…

A Completeness Theorem for Topological Doctrines
We extend logical categories with fiberwise interior and closure operators so as to obtain an embedding theorem into powers of the category of topological spaces. The required axioms, besides the Kuratowski closure axioms, are a `product independence' and a `loop contraction' principle.