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Littérature scientifique sur le sujet « Functorial interpretation »

Auteur : Grafiati

Publié le 7 juin 2025

Mis à jour le 2 août 2025

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Articles de revues sur le sujet "Functorial interpretation"

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DOMÍNGUEZ, CÉSAR, and DOMINIQUE DUVAL. "A PARAMETERIZATION PROCESS: FROM A FUNCTORIAL POINT OF VIEW." International Journal of Foundations of Computer Science 23, no. 01 (2012): 225–42. http://dx.doi.org/10.1142/s0129054112500050.

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The parameterization process used in the symbolic computation systems Kenzo and EAT is studied here as a general construction in a categorical framework. This parameterization process starts from a given specification and builds a parameterized specification by adding a parameter as a new variable to some operations. Given a model of the parameterized specification, each interpretation of the parameter, called an argument, provides a model of the given specification. Moreover, under some relevant terminality assumption, this correspondence between the arguments and the models of the given spec

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Ntelis, Pierros. "Advancing Tensor Theories." Symmetry 17, no. 5 (2025): 777. https://doi.org/10.3390/sym17050777.

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This paper advances the foundations of tensor and category theories by introducing novel concepts and rigorous constructive proofs. We generalize tensor theory through the innovative notion of a generalised tensor index, a versatile framework that unifies diverse tensor indices, and explore its transformation properties. Using fractional derivatives, we provide a geometrical interpretation of these generalised tensors, revealing new insights into its structure. Additionally, we forge a deep connection between tensor and category theories, integrating sets, tensors, categories, and functors wit

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Sakellaridis, Yiannis. "On the unramified spectrum of spherical varieties over p-adic fields." Compositio Mathematica 144, no. 4 (2008): 978–1016. http://dx.doi.org/10.1112/s0010437x08003485.

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AbstractThe description of irreducible representations of a group G can be seen as a problem in harmonic analysis; namely, decomposing a suitable space of functions on G into irreducibles for the action of G×G by left and right multiplication. For a split p-adic reductive group G over a local non-archimedean field, unramified irreducible smooth representations are in bijection with semisimple conjugacy classes in the ‘Langlands dual’ group. We generalize this description to an arbitrary spherical variety X of G as follows. Irreducible unramified quotients of the space $C_c^\infty (X)$ are in n

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Bespalov, Y. "Categories: Between Cubes and Globes. Sketch I." Ukrainian Journal of Physics 64, no. 12 (2019): 1125. http://dx.doi.org/10.15407/ujpe64.12.1125.

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For a finite partially ordered set I, we define an abstract polytope PI which is a cube or a globe in the cases of discrete or linear poset, respectively. For a poset P, we have built a small category ♦P with finite lower subsets in P as objects. This category ♦P = ♦P+♦P- is factorized into a product of two wide subcategories ♦P+ of faces and ♦P- of degenerations. One can imagine a degeneration from I to J ⊂ I as a projection of an abstract polytope PI to the subspace spanned by J. Morphisms in ♦P+ with fixed target I are identified with faces of PI . The composition in ♦P admits the natural g

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NEHANIV, CHRYSTOPHER LEV. "ALGEBRAIC CONNECTIVITY." International Journal of Algebra and Computation 01, no. 04 (1991): 445–71. http://dx.doi.org/10.1142/s0218196791000316.

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Let [Formula: see text] be a type of algebra in the sense of universal algebra. By defining singular simplices in algebras and emulating singular [co] homology, we introduce for each variety, pseudo-variety, and divisional class V of type [Formula: see text], a homology and cohomology theory which measure the V-connectivity of type-[Formula: see text] algebras. Intuitively, if we were to think of an algebra as a space and subalgebras which lie in V as simplices, then V-connectivity describes the failure of subalgebras to lie in V, i.e., it describes the "holes" in this space. These [co]homolog

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Katsumata, Shin-ya, Xavier Rival, and Jérémy Dubut. "A Categorical Framework for Program Semantics and Semantic Abstraction." Electronic Notes in Theoretical Informatics and Computer Science Volume 3 - Proceedings of... (November 23, 2023). http://dx.doi.org/10.46298/entics.12288.

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Categorical semantics of type theories are often characterized as structure-preserving functors. This is because in category theory both the syntax and the domain of interpretation are uniformly treated as structured categories, so that we can express interpretations as structure-preserving functors between them. This mathematical characterization of semantics makes it convenient to manipulate and to reason about relationships between interpretations. Motivated by this success of functorial semantics, we address the question of finding a functorial analogue in abstract interpretation, a genera

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DOTSENKO, VLADIMIR, and OISÍN FLYNN-CONNOLLY. "Three Schur functors related to pre-Lie algebras." Mathematical Proceedings of the Cambridge Philosophical Society, October 16, 2023, 1–18. http://dx.doi.org/10.1017/s0305004123000580.

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Abstract We give explicit combinatorial descriptions of three Schur functors arising in the theory of pre-Lie algebras. The first of them leads to a functorial description of the underlying vector space of the universal enveloping pre-Lie algebra of a given Lie algebra, strengthening the Poincaré-Birkhoff-Witt (PBW) theorem of Segal. The two other Schur functors provide functorial descriptions of the underlying vector spaces of the universal multiplicative enveloping algebra and of the module of Kähler differentials of a given pre-Lie algebra. An important consequence of such descriptions is a

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Evripidou, Charalampos Andreas, Pavlos Kassotakis, and Pol Vanhaecke. "Morphisms and automorphisms of skew-symmetric Lotka-Volterra systems." Journal of Physics A: Mathematical and Theoretical, July 5, 2022. http://dx.doi.org/10.1088/1751-8121/ac7e90.

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Abstract We study the basic relation between skew-symmetric Lotka-Volterra systems and graphs, both at the level of objects and morphisms, and derive a classification from it of skew-symmetric Lotka-Volterra systems in terms of graphs as well as in terms of irreducible weighted graphs. We also obtain a description of their automorphism groups and of the relations which exist between these groups. The central notion introduced and used is that of decloning of graphs and of Lotka-Volterra systems. We also give a functorial interpretation of the results which we obtain.

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Pinet, Théo. "A functor for constructing R$R$‐matrices in the category O$\mathcal {O}$ of Borel quantum loop algebras." Journal of the London Mathematical Society, September 14, 2023. http://dx.doi.org/10.1112/jlms.12815.

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AbstractWe tackle the problem of constructing ‐matrices for the category associated to the Borel subalgebra of an arbitrary untwisted quantum loop algebra . For this, we define an invertible exact functor from the category linked to to the one linked to . This functor is compatible with tensor products, preserves irreducibility, and interchanges the subcategories and of Hernandez and Leclerc (Algebra Number Theory 10 (2016) 2015–2052). We construct ‐matrices for by applying on the braidings already found for by Hernandez (Represent. Theory 26 (2022) 179–210). We also use the factorization of t

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VERA, ANDERSON. "Johnson–Levine homomorphisms and the tree reduction of the LMO functor." Mathematical Proceedings of the Cambridge Philosophical Society, November 27, 2019, 1–35. http://dx.doi.org/10.1017/s0305004119000410.

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Abstract Let $\mathcal{M}$ denote the mapping class group of Σ, a compact connected oriented surface with one boundary component. The action of $\mathcal{M}$ on the nilpotent quotients of π1(Σ) allows to define the so-called Johnson filtration and the Johnson homomorphisms. J. Levine introduced a new filtration of $\mathcal{M}$ , called the Lagrangian filtration. He also introduced a version of the Johnson homomorphisms for this new filtration. The first term of the Lagrangian filtration is the Lagrangian mapping class group, whose definition involves a handlebody bounded by Σ, and which conta

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Thèses sur le sujet "Functorial interpretation"

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Kang, Ning active 2013. "The functorial interpretation of the naive compactification of regular morphism from P¹ to P¹." Thesis, 2013. http://hdl.handle.net/2152/23293.

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Livres sur le sujet "Functorial interpretation"

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Bell, John L. Categorical Logic and Model Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0007.

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The chapter begins with an introduction describing the development of categorical logic from the 1960s. The next section, `Categories and Deductive Systems’, describes the relationship between categories and propositional logic, while the ensuing section, `Functorial Semantics’, is devoted to Lawvere’s provision of the first-order theory of models with a categorical formulation. In the section `Local Set Theories and Toposes’ the categorical counterparts—toposes—to higher-order logic are introduced, along with their associated theories—local set theories. In the section `Models of First-Order

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Chapitres de livres sur le sujet "Functorial interpretation"

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Goldstein, Stanisław, and Louis Labuschagne. "Abelian von Neumann algebras." In Noncommutative measures and Lp and Orlicz Spaces, with Applications to Quantum Physics. Oxford University PressOxford, 2025. https://doi.org/10.1093/oso/9780198950202.003.0003.

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Abstract This chapter serves to prepare the reader for the future interpretation of non-abelian von Neumann algebras as noncommutative L∞-spaces. We achieve this by presenting a proof of Maharam’s theorem interpreted from a von Neumann algebra perspective, which is in essence a structural classification of abelian von Neumann algebras. We then apply the resultant theory to show that abelian von Neumann algebras may variously be represented as L∞-spaces living on either localizable, decomposable or Radon measure spaces. As a consequence we then show that the categories of abelian von Neumann (m

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Yves, Diers. "Schemes." In Categories of Commutative Algebras. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198535867.003.0005.

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Abstract The localization process associates to any object a sheaf of local objects on its prime spectrum, while the globalization process rebuilds any object from the continuous family of its localized objects. By means of these processes, any object turns into a geometrical object: its affine scheme. By making these processes functorial, we obtain an equivalence between the category of affine schemes on a Zariski category A and the dual of A. Numerous properties of objects and morphisms in A have nice geometrical interpretations in the associated category of affine schemes. For example, a mo

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