Related papers: Morphisms (should be) everywhere
Multiparticle systems on complicated metric graphs might have many applications in physics, biology and social life. But the corresponding science still does not exist. Here we start it with simplest examples where there is quadratic…
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…
Pseudo-harmonic morphisms give rise on the domain space to a distribution which admits an almost complex structure compatible with the given Riemannian metric. We shall show that this property, together with the harmonicity, are preserved…
Parametricity states that polymorphic functions behave the same regardless of how they are instantiated. When developing polymorphic programs, Wadler's free theorems can serve as free specifications, which can turn otherwise partial…
We develop an extension of institution theory that accommodates implicitly the partiality of the signature morphisms and its syntactic and semantic effects. This is driven primarily by applications to conceptual blending, but other…
Maps between spaces of measures on measurable spaces $(X,\Sigma_X)$ and $(Y, \Sigma_Y)$ are treated as generalized functions between $X$ and $Y$.
Motivated by the intermediate Lang conjectures on hyperbolicity and rational points, we prove new finiteness results for non-constant morphisms from a fixed variety to a fixed variety defined over a number field by applying Faltings's…
In this paper we develop the theory of {\it polymorphisms} of measure spaces, which is a generalization of the theory of measure-preserving transformations; we describe the main notions and discuss relations to the theory of Markov…
The ability to reason with and integrate different sensory inputs is the foundation underpinning human intelligence and it is the reason for the growing interest in modelling multi-modal information within Knowledge Graphs. Multi-Modal…
The paper has two main goals. The first is to take a new approach to rearrangements on certain classes of measurable real-valued functions on $\mathbb{R}^n$. Rearrangements are maps that are monotonic (up to sets of measure zero) and…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
We describe an algorithm that morphs between two planar orthogonal drawings $\Gamma_I$ and $\Gamma_O$ of a connected graph $G$, while preserving planarity and orthogonality. Necessarily $\Gamma_I$ and $\Gamma_O$ share the same combinatorial…
We construct (in significant generality) moduli spaces representing the functor of morphisms from a scheme into a solvable algebraic group.
We give a valuative criterion for when a smooth algebraic stack with a separated good moduli space is the quotient of a separated Deligne-Mumford stack by a torus. For doing so, we introduce a new class of morphisms, the so-called effective…
We describe a procedure for constructing morphisms in additive categories, combining Auslander's concept of a morphism determined by an object with the existence of flat covers. Also, we show how flat covers are turned into projective…
Mathematical morphology (MM) helps to describe and analyze shapes using set theory. MM can be effectively applied to binary images which are treated as sets. Basic morphological operators defined can be used as an effective tool in image…
The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical…
The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…