Monoidal context theory

M Román - arxiv preprint arxiv:2404.06192, 2024 - arxiv.org
We universally characterize the produoidal category of monoidal lenses over a monoidal
category. In the same way that each category induces a cofree promonoidal category of …

An invitation to higher arity science

C Zapata-Carratalá, XD Arsiwalla - arxiv preprint arxiv:2201.09738, 2022 - arxiv.org
Analytical thinking is dominated by binary ideas. From pair-wise interactions, to algebraic
operations, to compositions of processes, to network models, binary structures are deeply …

Clones, closed categories, and combinatory logic

P Saville - International Conference on Foundations of Software …, 2024 - Springer
We explain how to recast the semantics of the simply-typed λ-calculus, and its linear and
ordered variants, using multi-ary structures. We define universal properties for …

On Quantifiers for Quantitative Reasoning

M Capucci - arxiv preprint arxiv:2406.04936, 2024 - arxiv.org
We explore a kind of first-order predicate logic with intended semantics in the reals.
Compared to other approaches in the literature, we work predominantly in the multiplicative …

Bifibrations of polycategories and classical multiplicative linear logic

N Blanco - arxiv preprint arxiv:2305.15139, 2023 - arxiv.org
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying
how to express certain categorical structures as universal properties by generalising the …

Compositional frameworks for supermaps and causality

M Wilson - 2023 - ora.ox.ac.uk
Quantum supermaps are transformations of quantum processes, and have found many
applications in quantum foundations and quantum information theory in the past two …

[PDF][PDF] Notes on profunctors and compact multiplicative linear logic

C Comfort - 2024 - colecomfort.github.io
In [WGZ22] they reprove the coherence theorem for monoidal categories; constructing a
strict monoidal category which is monoidally equivalent to a given monoidal category by …