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The unreasonable power of the lifting property in elementary mathematics
Gavrilovich M.
We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a number of examples in various categories, in particular showing that many standard elementary notions of abstract topology can be defined by applying the lifting property to simple morphisms of finite topological spaces. Examples in topology include the notions of: compact, discrete, connected, and totally disconnected spaces, dense image, induced topology, and separation axioms. Examples in algebra include: finite groups being nilpotent, solvable, torsion-free, p-groups, and prime-to-p groups; injective and projective modules; injective, surjective, and split homomorphisms. We include some speculations on the wider significance of this.
Publication based on the results of:
Lukacheva S., Zakharova E., Makhaneva A. et al., Journal of Solid State Chemistry 2025 Vol. 345 Article 125223
A new gallium-rich intermetallic Ti2-xNi3Ga9 was synthesized by high-temperature techniques as bulk samples and single crystals. The composition and structure of the compound were established by a combination of single-crystal and powder X-ray analysis and energy-dispersive X-ray spectroscopy. The obtained intermetallic compound crystallizes in its own structure type and has a narrow homogeneous region of ...
Added: February 23, 2026
Batanin M., White D., Journal of Pure and Applied Algebra 2024 Vol. 228 No. 6 Article 107570
Given a combinatorial (semi-)model category M and a set of morphisms C, we establish the existence of a semi-model category LCM satisfying the universal property of the left Bousfield localization in the category of semi-model categories. Our main tool is a semi-model categorical version of a result of Jeff Smith, that appears to be of ...
Added: December 26, 2025
Dragalina-Chernaya E., Логические исследования 2025 Т. 31 № 2 С. 9–30
В статье предлагается интерпретация абстрактных логик как классификаций абстрактных структур (типов изоморфизма). Свойство инвариантности относительно изоморфизма понимается не как традиционный
критерий демаркации логических и нелогических терминов, а как мета-ограничение на соответствующие
классы структур. Выявляется вариативность подобных мета-ограничений в ранней и современной теории моделей. Сопоставляются онтологические подходы, предполагающие трактовку абстрактной структуры как формы, разделяемой всеми структурами в данном типе ...
Added: September 8, 2025
Arzhantsev I., Petravchuk A. P., Mathematical notes 2009 Vol. 86 No. 5 P. 625–628
Every subfield K(φ) of the field of rational fractions K(x_1, . . . , x_n) is contained in a unique maximal subfield of the form K(ψ). The element ψ is said to be generating for the element φ. A subfield of K(x_1, . . . , x_n) is said to be saturated if, together with ...
Added: June 13, 2025
Farjoun E. D., Ivanov S. O., Krasilnikov A. et al., Journal of Algebra 2025 Vol. 675 P. 273–288
We consider several types of non-existence theorems for functors. For example, there are no nontrivial functors from the category of groups (or the category of pointed sets, or vector spaces) to any small category. In addition, we consider questions about nonexistence of subfunctors and quotients of the identity functor on the category of groups (or ...
Added: May 5, 2025
Дюканов П. А., Kozhukhov M., Popov D. et al., Успехи прикладной физики 2024 Т. 12 № 4 С. 334–342
The paper considers options for the design of an n-channel junction-gate field-effect transistor, integrated into a high-voltage complementary bipolar technological process with isolation by a reverse-biased p-n junction. Criteria for the selection of transistor models according to electrophysical parameters are formulated. Taking into account the criteria, the instrument-technological modeling on bulk silicon substrates was carried ...
Added: September 12, 2024
Mikhail Yu. Romashikhin, , in: Proceedings 2024 International Russian Smart Industry Conference (SmartIndustryCon), 25-29 March 2024.: Sochi: IEEE, 2024. P. 104–108.
This article describes the implementation of regular topologies for networks-on-chip. The complexity of network development and its main parameters depend on the choice of topology. The rationale for the influence of topology on network bandwidth is given. Software that automates the generation of configuration files (bitstream) for the implementation of networks-on-chip with different topologies and ...
Added: May 13, 2024
Krenke A., Sandlerskiy R., Baibar A. et al., Известия РАН. Серия биологическая 2023 № 7 С. 93–108
A brief review of the main models for emergence of boundaries and, in a particular case, integrity, arising from the theory of nonlinear volumetric systems. Based on the fundamental value of Kotelnikov’s reference and, accordingly, the general theory of awareness about identifying a characteristic border feature, as frequency of sampling functions in incidence along with ...
Added: December 9, 2023
Prokhorov Y., , in: 8th European Congress of Mathematics, Portorož, 20–26 June, 2021.: [б.и.], 2023. P. 413–437.
We survey new results on finite groups of birational transformations of algebraic varieties. ...
Added: November 13, 2023
Dragalina-Chernaya E., , in: 4th Lisbon International Conference on Philosophy of Science - LICPOS 2023.: Lisbon: CFCUL, 2023. P. 27–28.
This paper offers an interpretation of abstract logics as formal ontologies as well as higher-level classifications. ...
Added: July 14, 2023
Gogoleva N., Zorina-Tikhonova E., Khapaeva P. et al., Journal of Molecular Structure 2022 Vol. 1256 Article 132532
A series of cobalt(II) and cadmium(II) compounds comprising dimethylmalonate anions combined with potassium and barium ions have been synthesized. The compounds obtained are coordination polymers with 3D structure (1) or 2D structure (2–4). It has been shown that, depending on the nature of heterometals, the type of coordination of dimethylmalonic acid by d-metal atoms changes: from ...
Added: January 24, 2023
A. N. Krenke, R. B. Sandlersky, A. S. Baybar et al., Известия РАН. Серия биологическая. 2023 Vol. 50 No. 1 P. S85–S99
Four main models of the appearance of boundaries (in a particular case, integrity), arising from the theory of nonlinear dynamic systems, are considered briefly. On the basis of Kotelnikov’s fundamental sampling theorem and, accordingly, general information theory, the character of a distinguished boundary as a function of the sampling frequency in a spatial series with a ...
Added: December 2, 2022
Antonina A. Arkhipova, Ivanov S., Zhuravitskii S. et al., Nanophotonics 2022 Vol. 11 No. 16 P. 3653–3661
We report the experimental observation of the periodic switching of topological edge states between two dimerized fs-laser written waveguide arrays. Switching occurs due to the overlap of the modal fields of the edge states from topological forbidden gap, when they are simultaneously present in two arrays brought into close proximity. We found that the phenomenon ...
Added: October 17, 2022
Raikov A., Pirani M., IEEE Access 2022 Vol. 10 P. 56296–56315
The goal of the paper is to find means for the unification of human-machine duality in collective behavior of people and machines, by conciliating approaches that proceed in opposite directions. The first approach proceeds top-down from non-formalizable, cognitive, uncaused, and chaotic human consciousness towards purposeful and sustainable human-machine interaction. The second approach proceeds bottom-up from ...
Added: July 19, 2022
Letellier C., Stankevich N., Rössler O., International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2022 Vol. 32 No. 2 Article 2230004
Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their labeling. Addressing these problems corresponds to the development of a dynamical taxonomy, exhibiting the key properties discriminating the variety ...
Added: February 24, 2022
Kachan O., , in: 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW).: IEEE, 2020. P. 3744–3751.
Dimensionality reduction problem is stated as finding a mapping f:X ∈ R m → Z ∈ R n , where ≪ m while preserving some relevant properties of the data. We formulate topology-preserving dimensionality reduction as finding the optimal orthogonal projection to the lower-dimensional subspace which minimizes discrepancy between persistent diagrams of the original data and the projection. This ...
Added: December 12, 2021
Prokhorov Y., / Series arXiv "math". 2021.
We survey new results on finite groups of birational transformations of algebraic varieties. ...
Added: November 25, 2021
Polotovskiy G., В кн.: Классическая и современная геометрия. Материалы Международной конференции, посвященной 100-летию со дня рождения Л.С. Атанасяна (Москва, 1–4 ноября 2021 г.).: М.: МПГУ, 2021. С. 125–126.
Очерк истории топологического образования в Нижнем Новгороде ...
Added: October 31, 2021
Арутюнов А. А., Kosolapov L., Finite Fields and Their Applications 2021 Vol. 76 Article 101921
In this paper we establish decomposition theorems for derivations of group rings. We provide a topological technique for studying derivations of a group ring A[G] in case G has finite conjugacy classes. As a result, we describe all derivations of algebra A[G] for the case when G is a finite group, or G is an FC-group. In addition, we describe an algorithm to explicitly calculate all derivations of ...
Added: October 4, 2021
Rzaev E., Romanov A., , in: 2021 International Russian Automation Conference (RusAutoCon).: IEEE, 2021. P. 421–425.
Added: September 25, 2021
Shramov K., European Journal of Mathematics 2021 Vol. 7 P. 591–612
We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi–Brauer surfaces over fields of characteristic zero. ...
Added: September 8, 2021
Rumynin D., Taylor J., Linear Algebra and its Applications 2021 Vol. 610 P. 135–168
We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite C_2-graded groups. A finite C_2-graded group is a finite group with a subgroup of index 2. In this theory the subgroup acts linearly, while the other coset acts antilinearly. We introduce antilinear blocks, whose structure is a crucial ...
Added: September 7, 2021
Glazov M., Поддубный А. Н., Physical Review Letters 2019 Vol. 123 P. 126801
We theoretically study Rydberg excitons in one-dimensional chains of traps in Cu2O coupled via the van der Waals interaction. The triplet of optically active p-shell states acts as an effective spin 1, and the interactions between the excitons are strongly spin dependent. We predict that the system has the topological Haldane phase with the diluted antiferromagnetic ...
Added: January 13, 2021