Related papers: Pointwise extensions and sketches in bicategories
Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…
We study the representability of sets that admit extended formulations using mixed-integer bilevel programs. We show that feasible regions modeled by continuous bilevel constraints (with no integer variables), complementarity constraints,…
We introduce a categorical formalism for rewriting surface-embedded graphs. Such graphs can represent string diagrams in a non-symmetric setting where we guarantee that the wires do not intersect each other. The main technical novelty is a…
Categorial methods for generating new local algebras from old ones are presented. A direct proof of the differential structure of the prolongations of a manifold is proposed.
We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…
We provide multiple combinatorial expansion formulas - in terms of snake graphs, labelled posets, matrices, and $T$-walks - for elements in generalized cluster algebras associated to arcs on punctured orbifolds and illustrate their…
We study the problem of when triangulated categories admit unique infinity-categorical enhancements. Our results use Lurie's theory of prestable infinity-categories to give conceptual proofs of, and in many cases strengthen, previous work…
We establish a new extension result for twisted canonical forms defined on a hypersurface with simple normal crossings of a projective manifold. Some of the examples presented in the appendix are showing that the bounds we obtain for the…
We establish a bi-equivalence between the bi-category of topoi with enough points and a localisation of a bi-subcategory of topological groupoids
We present a general procedure for constructing triangulated categories, linear over a field, with distinct enhancements. Some of our examples can be equipped with a (non-degenerate) t-structure, thereby showing that the existence of a…
We offer two proofs that categories weakly enriched over symmetric monoidal categories can be strictified to categories enriched in permutative categories. This is a "many 0-cells" version of the strictification of bimonoidal categories to…
This is a short survey illustrating some of the essential aspects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices with additional operations in finitely generated varieties…
Metric approximate categories, or metagories, for short, are metrically enriched graphs. Their structure assigns to every directed triangle in the graph a value which may be interpreted as the area of the triangle; alternatively, as the…
Building on the notion of normed category as suggested by Lawvere, we introduce notions of Cauchy convergence and cocompleteness which differ from proposals in previous works. Key to our approach is to treat them consequentially as…
We introduce the homogeneous and piecewise multilinear extensions and the eigenvalue problem for locally Lipschitz function pairs, in order to develop a systematic framework for relating discrete and continuous min-max problems. This also…
We introduce boundary special generic maps, a class of submersions from manifolds with boundary to Euclidean spaces whose restriction to the boundary has only boundary definite fold points as its singular points. We derive the…
State of the art language models return a natural language text continuation from any piece of input text. This ability to generate coherent text extensions implies significant sophistication, including a knowledge of grammar and semantics.…
This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…
In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory. It turns out that many categorial properties are well behaved under…
We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our…