Related papers: Consciousness in a Higher Categorical Context
A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion…
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.…
Deep models that are both effective and explainable are desirable in many settings; prior explainable models have been unimodal, offering either image-based visualization of attention weights or text-based generation of post-hoc…
This is the first draft of a book about higher categories approached by iterating Segal's method, as in Tamsamani's definition of $n$-nerve and Pelissier's thesis. If $M$ is a tractable left proper cartesian model category, we construct a…
Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…
We assume that substances in the world are represented by two types of concepts, namely substance concepts and classification concepts, the former instrumental to (visual) perception, the latter to (language based) classification. Based on…
We use the terms "$\infty$-categories" and "$\infty$-functors" to mean the objects and morphisms in an "$\infty$-cosmos." Quasi-categories, Segal categories, complete Segal spaces, naturally marked simplicial sets, iterated complete Segal…
We introduce \emph{flagged $(\infty,n)$-categories} and prove that they are equivalent to Segal sheaves on Joyal's category ${\mathbf\Theta}_n$. As such, flagged $(\infty,n)$-categories provide a model-independent formulation of Segal…
We discuss that there exist at least two different choices in the signs of the induced A-infinity structures in shifting the degree of objects in an A-infinity category. We show that both of these choices are naturalin the sense that they…
Let $\mathcal{X}$ be a semibrick in an extriangulated category $\mathscr{C}$. Let $\mathcal{T}$ be the filtration subcategory generated by $\mathcal{X}$. We give a one-to-one correspondence between simple semibricks and length wide…
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…
We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as a potential yoga for dealing with processes and processes of…
Lifts of categorical diagrams $D\colon\mathsf{J}\to\mathsf{X}$ against discrete opfibrations $\pi\colon\mathsf{E}\to\mathsf{X}$ can be interpreted as presenting solutions to systems of equations. With this interpretation in mind, it is…
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
We define 2-categories of microlocal perverse (resp. coherent) sheaves of categories on the skeleton of a hypertoric variety and show that the generators of these 2-categories lift the projectives (resp. simples) in hypertoric category…
We cast aspects of consciousness in axiomatic mathematical terms, using the graphical calculus of general process theories (a.k.a symmetric monoidal categories and Frobenius algebras therein). This calculus exploits the ontological…
We investigate the position that foundational theories should be modelled on ordinary computability. In this context, we investigate the metamathematics of $\Sigma$ formulas. We consider theories whose axioms are implications between…
Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is…
Categorical spectra are spectrum objects in pointed $(\infty,\infty)$-categories: sequences $(X_n)$ equipped with equivalences $X_n\simeq \Omega X_{n+1}$. This thesis develops foundations for categorical spectra and constructs their tensor…
We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem…