Related papers: Consciousness in a Higher Categorical Context
We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…
In many scenarios, human decisions are explained based on some high-level concepts. In this work, we take a step in the interpretability of neural networks by examining their internal representation or neuron's activations against concepts.…
Self-explaining text categorization requires a classifier to make a prediction along with supporting evidence. A popular type of evidence is sub-sequences extracted from the input text which are sufficient for the classifier to make the…
Given a family of model categories $\cal E \to \cal C$, we associate to it a homotopical category of derived, or Segal, sections $DSect(\cal C,\cal E)$ that models the higher-categorical sections of the localisation $L\cal E \to \cal C$.…
We develop a 2-dimensional version of accessibility and presentability compatible with the formalism of flat pseudofunctors. First we give prerequisites on the different notions of 2-dimensional colimits, filteredness and cofinality; in…
In the last years the debate on complexity has been developing and developing in transdisciplinary way to meet the need of explanation for highly organized collective behaviors and sophisticated hierarchical arrangements in physical,…
We develop axiomatics of highest weight categories and quasi-hereditary algebras in order to incorporate two semi-infinite situations which are in Ringel duality with each other; the underlying posets are either upper finite or lower…
We present an efficient and user-friendly method for constructing any cofibrantly generated model structure on the category of double categories whose trivial fibrations are the "canonical" ones: the double functors which are surjective on…
This contribution examines two radically different explanations of our phenomenal intuitions, one reductive and one strongly non-reductive, and identifies two germane ideas that could benefit many other theories of consciousness. Firstly,…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
In this paper, we go into the study of the 2-category SSS_\Sigma of \Sigma-constructible stacks. The notions of constructible stack was introduced by D. Treumann. It is a natural generalization of constructible sheaf. D. Treumann has also…
In this paper we give a summary of the comparisons between different definitions of so-called (\infty,1)-categories, which are considered to be models for \infty-categories whose n-morphisms are all invertible for n>1. They are also, from…
The rapid evolution of multimodal foundation model has demonstrated significant progresses in vision-language understanding and generation, e.g., our previous work SEED-LLaMA. However, there remains a gap between its capability and the…
Inverse categories are categories in which every morphism x has a unique pseudo-inverse y in the sense that xyx=x and yxy=y. Persistence modules from topological data analysis and similarly decomposable category representations factor…
This paper introduces a unifying framework that links the Context-Content Uncertainty Principle (CCUP) with optimal transport (OT) via primal-dual inference. We propose that cognitive representations are not static encodings but active dual…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
Real-world data often follows a long-tailed distribution, which makes the performance of existing classification algorithms degrade heavily. A key issue is that samples in tail categories fail to depict their intra-class diversity. Humans…
We propose a sequential topology on the space of sub-$\sigma$-algebras of a separable probability space $(\Omega,\mathcal{F},\mathbb{P})$ by linking conditional expectations on $L^{2}$ along sequences of sub-$\sigma$-algebras. The varying…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…