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Weighted bipolar argumentation frameworks offer a tool for decision support and social media analysis. Arguments are evaluated by an iterative procedure that takes initial weights and attack and support relations into account. Until…
This article develops a theory of cell combinatorics and cell 2-representations for differential graded 2-categories. We introduce two types of partial preorders, called the strong and weak preorder. We then analyse and compare them. The…
String diagrams are pictorial representations for morphisms of symmetric monoidal categories. They constitute an intuitive and expressive graphical syntax, which has found application in a very diverse range of fields including concurrency…
Diffusion Transformers have achieved state-of-the-art performance in class-conditional and multimodal generation, yet the structure of their learned conditional embeddings remains poorly understood. In this work, we present the first…
We construct a `weak' version EM^w(K) of Lack & Street's 2-category of monads in a 2-category K, by replacing their compatibility constraint of 1-cells with the units of monads by an additional condition on the 2-cells. A relation between…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Modelling musical structure is vital yet challenging for artificial intelligence systems that generate symbolic music compositions. This literature review dissects the evolution of techniques for incorporating coherent structure, from…
We want to replace categories, functors and natural transformations by categories, open functors and open natural transformations. In analogy with open dynamical systems, the adjective open is added here to mean that some external…
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…
Bidirectional causal relationships arising from mutual interactions between variables are commonly observed within biomedical, econometrical, and social science contexts. When such relationships are further complicated by unobserved…
This paper introduces a novel approach to multi-parameter persistence using 2-categorical structures. We develop a framework that captures hierarchical interactions between filter parameters, overcoming fundamental limitations of…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
The recently introduced model of representations has been defined and motivated somewhat ex-nihilo. In this document, I will show that representations are related to a more ''classical'' model through a 2-adjunction. The target model is…
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
We introduce bimonads in a 2-category $\K$ and define biwreaths as bimonads in the 2-category $\bEM(\K)$ of bimonads, in the analogous fashion as Lack and Street defined wreaths. A biwreath is then a system containing a wreath, a cowreath…
This work studies the representational mapping across multimodal data such that given a piece of the raw data in one modality the corresponding semantic description in terms of the raw data in another modality is immediately obtained. Such…
Recently, there has been growing interest in bicategorical models of programming languages, which are "proof-relevant" in the sense that they keep distinct account of execution traces leading to the same observable outcomes, while assigning…
Virtual double categories provide an effective framework for formal category theory. Recent work has investigated the question of higher morphisms between virtual double categories, following on from work on higher morphisms between double…
Multimodal models have been proven to outperform text-based models on learning semantic word representations. Almost all previous multimodal models typically treat the representations from different modalities equally. However, it is…
Even a functor without an adjoint induces a monad, namely, its codensity monad; this is subject only to the existence of certain limits. We clarify the sense in which codensity monads act as substitutes for monads induced by adjunctions. We…