Related papers: Effectful Semantics in Bicategories: Strong, Commu…
The category of open games, which provides a strongly compositional foundation of economic game theory, is intermediate between symmetric monoidal and compact closed. More precisely it has counits with no corresponding units, and a…
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…
We provide a complete generators and relations presentation of the 2-dimensional extended unoriented and oriented bordism bicategories as symmetric monoidal bicategories. Thereby we classify these types of 2-dimensional extended topological…
Let $A$ be a ring and $\M_A$ the category of $A$-modules. It is well known in module theory that for any $A $-bimodule $B$, $B$ is an $A$-ring if and only if the functor $-\otimes_A B: \M_A\to \M_A$ is a monad (or triple). Similarly, an $A…
Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory. Motivated by constructions needed in…
Language models famously improve under a smooth scaling law, but some specific capabilities exhibit sudden breakthroughs in performance. Advocates of "emergence" view these capabilities as unlocked at a specific scale, but others attribute…
We prove coherence theorems for bicategories, pseudofunctors and pseudonatural transformations. These theorems boil down to proving the coherence of some free $(4,2)$-categories. In the case of bicategories and pseudofunctors, existing…
Neural networks often pack many unrelated concepts into a single neuron - a puzzling phenomenon known as 'polysemanticity' which makes interpretability much more challenging. This paper provides a toy model where polysemanticity can be…
Most often, in a categorical semantics for a programming language, the substitution of terms is expressed by composition and finite products. However this does not deal with the order of evaluation of arguments, which may have major…
Supervenience is an important philosophical concept. In this paper, inspired by the supervenience-determined consequence relation and the semantics of agreement operator, we introduce a modal logic of supervenience, which has a dyadic…
We prove that steady state bifurcations in finite-dimensional dynamical systems that are symmetric with respect to a monoid representation generically occur along an absolutely indecomposable subrepresentation. This is stated as a…
The notion of pseudocategory, as considered in [11], is extended from the context of a 2-category to the more general one of a sesquicategory, which is considered as a category equipped with a 2-cell structure. Some particular examples of…
A conjecture of May states that there is an up-to-adjunction strictification of symmetric bimonoidal functors between bipermutative categories. The main result of this paper proves a weaker form of May's conjecture that starts with…
In this paper we present an analytical and numerical study of a generalized model of two-actor cooperative-competitive conflict of the Continuous Opinions and Discrete Actions (CODA) type. Theoretically, we note that the in troduction of a…
The recent success of large foundation models in artificial intelligence has prompted the emergence of chemical pre-trained models. Despite the growing interest in large molecular pre-trained models that provide informative representations…
The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the…
In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…
The unification of low-level perception and high-level reasoning is a long-standing problem in artificial intelligence, which has the potential to not only bring the areas of logic and learning closer together but also demonstrate how…
Free monads (and their variants) have become a popular general-purpose tool for representing the semantics of effectful programs in proof assistants. These data structures support the compositional definition of semantics parameterized by…
Change detection is the study of detecting changes between two different images of a scene taken at different times. By the detected change areas, however, a human cannot understand how different the two images. Therefore, a semantic…