Related papers: Differential restriction categories
We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…
Adhesive categories provide an abstract framework for the algebraic approach to rewriting theory, where many general results can be recast and uniformly proved. However, checking that a model satisfies the adhesivity properties is sometimes…
Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including…
Many kinds of categorical structure require the existence of finite limits, of colimits of some specified type, and of "exactness" conditions between the finite limits and the specified colimits. Some examples are the notions of regular, or…
Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, lead to all the others without further recourse to topology.…
In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…
We propose a generalization of Categorial Grammar in which lexical categories are defined by means of recursive constraints. In particular, the introduction of relational constraints allows one to capture the effects of (recursive) lexical…
We analyse limits and colimits in the category $Part$ of partial groups, algebraic structures introduced by A. Chermak. We will prove that $Part$ is both complete and cocomplete and, in addition, that the full subcategory of finite partial…
We discuss a relation between the structure of derived categories of smooth projective varieties and their birational properties. We suggest a possible definition of a birational invariant, the derived category analogue of the intermediate…
We give a unified direct proof of the lifting of PIE limits to the 2-category of algebras and (pseudo) morphisms, which specifies precisely which of the projections of the lifted limit are strict and detect strictness. In the literature,…
Axial algebras are a recently introduced class of non-associative algebra motivated by applications to groups and vertex-operator algebras. We develop the structure theory of axial algebras focussing on two major topics: (1) radical and…
We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…
It is proved that MacLane's coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…
The term ``Boolean category'' should be used for describing an object that is to categories what a Boolean algebra is to posets. More specifically, a Boolean category should provide the abstract algebraic structure underlying the proofs in…
A new construction to associate an internal category to an enriched one is presented. The key concept is that of extensive ambient category, and the construction follows the one that associates a category whose idempotents split to a given…
It is proved that equalities between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equality in the language of free cartesian categories collapses a cartesian category into a preorder. An…
We note that large classes of contractions of algebras that arise in physics can be understood purely algebraically, via identifying appropriate $\mathbb{Z}_m$-gradings (and their generalizations) on the parent algebra. This includes…
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…