Related papers: Sketchable infinity categories
This paper develops a theory of colimit sketches "with constructions" in higher category theory, formalising the input to the ubiquitous procedure of adjoining specified "constructible" colimits to a category such that specified "relation"…
A theory of sketches for arithmetic universes (AUs) is developed. A restricted notion of sketch, called here "context", is defined with the property that every non-strict model is uniquely isomorphic to a strict model. This allows us to…
Free-hand sketches are appealing for humans as a universal tool to depict the visual world. Humans can recognize varied sketches of a category easily by identifying the concurrence and layout of the intrinsic semantic components of the…
We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the study of presentability ranks, a notion of cardinality…
We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. This generalization is intended for applications in the…
In this paper we prove that various quasi-categories whose objects are $\infty$-categories in a very general sense are complete: admitting limits indexed by all simplicial sets. This result and others of a similar flavor follow from a…
Inspired by the theory of classifying topoi for geometric theories, we define rounded sketches and logoi and provide the notion of classifying logos for a rounded sketch. Rounded sketches can be used to axiomatise all the known fragments of…
Freehand line sketches are an interesting and unique form of visual representation. Typically, such sketches are studied and utilized as an end product of the sketching process. However, we have found it instructive to study the sketches as…
We show first that derivators can be seen as models of a suitable homotopy limit 2-sketch. After discussing homotopy local $\lambda$-presentability of the 2-category of derivators, for some appropriate regular cardinal $\lambda$, as an…
We argue that locally Cartesian closed categories form a suitable doctrine for defining dependent type theories, including non-extensional ones. Using the theory of sketches, one may define syntactic categories for type theories in a style…
We present a generative model which can automatically summarize the stroke composition of free-hand sketches of a given category. When our model is fit to a collection of sketches with similar poses, it discovers and learns the structure…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
For a (possibly large) realized limit sketch $\mathcal{S}$ such that every $\mathcal{S}$-model is small in a suitable sense we show that the category of cocontinuous functors $\mathsf{Mod}(\mathcal{S}) \to \mathcal{C}$ into a cocomplete…
With the involvement of artificial intelligence (AI), sketches can be automatically generated under certain topics. Even though breakthroughs have been made in previous studies in this area, a relatively high proportion of the generated…
Generalizing different variants of "graph conditions and constraints" as well as "universal constraints" and "negative universal constraints" in the Diagram Predicate Framework (DPF), we introduce for arbitrary categories $\mathbf{Cxt}$ and…
Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in…
We construct the universal realized limit sketch associated to a given limit sketch. The construction uses factorization systems to organize the classical argument of [2], yielding a streamlined and conceptually unified formulation of the…
In this paper, we explore the unique modality of sketch for explainability, emphasising the profound impact of human strokes compared to conventional pixel-oriented studies. Beyond explanations of network behavior, we discern the genuine…
This paper introduces sketch-oriented databases, a categorical framework that encodes database paradigms as finite-limit sketches and individual databases and schemas as set-valued models. It illustrates the formalism through graph-oriented…
We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are…