相关论文: Generalized existential completions and their regu…

We use a category-theoretic formulation of Aczel's Fullness Axiom from Constructive Set Theory to derive the local cartesian closure of an exact completion. As an application, we prove that such a formulation is valid in the homotopy…

For conformal geometries of Riemannian signature, we provide a comprehensive and explicit treatment of the core local theory for embedded submanifolds of arbitrary dimension. This is based in the conformal tractor calculus and includes a…

Based on the intuitive notion of convexity, we formulate a universal property defining interval objects in a category with finite products. Interval objects are structures corresponding to closed intervals of the real line, but their…

The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…

We present generalized algebraic theories corresponding to slightly modified versions of two of the type theories in our paper Type Theory with Explicit Universe Polymorphism. We first present a generalized algebraic theory for categories…

We contribute to the knowledge of the quantifier completions and their applications by using the language of doctrines. This algebraic presentation allows us to properly analyse the behaviour of the existential and universal quantifiers. We…

A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by…

We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…

Existential rules are a prominent formalism to enrich a database with knowledge from the domain of interest, but make even basic reasoning tasks on the resulting knowledge base undecidable. To circumvent this, several classes of rules…

We develop a homotopy theory for additive categories endowed with endofunctors, analogous to the concept of a model structure. We use it to construct the homotopy theory of a Hovey triple (which consists of two compatible complete cotorsion…

We classify the propositional modal validities arising from the category of sets under its natural classes of morphisms. The resulting validities depend on the morphism class, the size of the world, and the permitted substitution instances.…

We explore the topological full group [[G]] of an essentially principal etale groupoid G on a Cantor set. When G is minimal, we show that [[G]] (and its certain normal subgroup) is a complete invariant for the isomorphism class of the etale…

Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its applicability to a variety of type systems, its error reporting, and its ease of implementation. Following…

This paper studies a general notion of flatness in the enriched context: P-flatness where the parameter P stands for a class of presheaves. One obtains a completion of a category A by considering the category Flat_P(A) of P-flat presheaves…

We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. Our main theorem proves a kind of finite generation, which in turn implies the existence of a ``universal generating…

Let $(\mathcal{A},\mathcal{E})$ be an exact category. We establish basic results that allow one to identify sub(bi)functors of $\operatorname{Ext}_{\mathcal{E}}(-,-)$ using additivity of numerical functions and restriction to subcategories.…

In this paper,the concepts of generalized ideal inf-limit and generalized ideal final lower bound limit are introduced in the directed complete poset,and their relations with Scott topology and Lawson topology are studied. The main results…

Homotopy limits and colimits are homotopical replacements for the usual limits and colimits of category theory, which can be approached either using classical explicit constructions or the modern abstract machinery of derived functors. Our…

Semiadditivity of an $\infty$-category, i.e. the existence of biproducts, provides it with useful algebraic structure in the form of a canonical enrichment in commutative monoids. This ultimately comes from the fact that the…

We present a domain-specific type theory for constructions and proofs in category theory. The type theory axiomatizes notions of category, functor, profunctor and a generalized form of natural transformations. The type theory imposes an…