相关论文: Realization of relational presheaves

The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…

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…

To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued…

We introduce the abstract setting of presheaf category on a thick category of cubes. Precubical sets, symmetric transverse sets, symmetric precubical sets and the new category of (non-symmetric) transverse sets are examples of this…

A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…

In this paper, we introduce a method to construct new categories which look like "cubes", and discuss model structures on the presheaf categories over them. First, we introduce a notion of thin-powered structure on small categories, which…

The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in mainstream empirical language processing tasks. We show how this approach can be generalized to…

Categorical semantics of type theories are often characterized as structure-preserving functors. This is because in category theory both the syntax and the domain of interpretation are uniformly treated as structured categories, so that we…

We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…

We introduce the notion of a Lie superheaps as a generalisation of Lie supergroups. We show that the well-known `groupification' and `heapification' functors generalise to the ambience of supergeometry. In particular, we show that there is…

Relation Extraction (RE) is a pivotal task in automatically extracting structured information from unstructured text. In this paper, we present a multi-faceted approach that integrates representative examples and through co-set expansion.…

We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of bounded operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a…

We introduce a notion of representation for a class of generalised quivers known as Coxeter quivers. These representations are built using fusion categories associated to $U_q(\mathfrak{s}\mathfrak{l}_2)$ at roots of unity and we show that…

We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of…

Motivated by potential applications to theoretical computer science, in particular those areas where the Curry-Howard correspondence plays an important role, as well as by the ongoing search in pure mathematics for feasible approaches to…

There are many category-theoretic notions of algebraic theory, including Lawvere theories, monads, PROPs and operads. The first central notion of this thesis is a common generalisation of these, which we call a proto-theory. In order to…

Staton has shown that there is an equivalence between the category of presheaves on (the opposite of) finite sets and partial bijections and the category of nominal restriction sets: see [2, Exercise 9.7]. The aim here is to see that this…

We develop foundations for oriented category theory, an extension of $(\infty,\infty)$-category theory obtained by systematic usage of the Gray tensor product, in order to study lax phenomena in higher category theory. As categorical…

Sequence-to-sequence (seq2seq) models are prevalent in semantic parsing, but have been found to struggle at out-of-distribution compositional generalization. While specialized model architectures and pre-training of seq2seq models have been…

We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to…