Results 21 to 30 of about 6,079,487 (235)
Brain's geometries for movements and beauty judgments. A contribution of topos geometries [PDF]
Frontiers in PsychologyWe present a theory on the neural basis of aesthetic experience, and judgment of beauty. It is based on both empirical facts concerning brain mechanisms and theoretical mathematical theories.
Daniel Bennequin, Alain Berthoz
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Shared Protentions in Multi-Agent Active Inference [PDF]
EntropyIn this paper, we unite concepts from Husserlian phenomenology, the active inference framework in theoretical biology, and category theory in mathematics to develop a comprehensive framework for understanding social action premised on shared goals.
Mahault Albarracin +5 more
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Transfinite limits in topos theory
Theory and Applications of Categories, 2015 For a coherent site we construct a canonically associated enlarged coherent site, such that cohomology of bounded below complexes is preserved by the enlargement.
M. Kerz
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Category-Theoretical and Topos-Theoretical Frameworks in Machine Learning: A Survey
AxiomsIn this survey, we provide an overview of category theory-derived machine learning from four mainstream perspectives: gradient-based learning, probability-based learning, invariance and equivalence-based learning, and topos-based learning.
Yiyang Jia +3 more
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On the ∞$\infty$ ‐topos semantics of homotopy type theory [PDF]
Bulletin of the London Mathematical Society, 2022 Many introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set‐based foundations. This expository article, written as lecture notes to accompany a three‐part mini course delivered
E. Riehl +5 more
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A Grothendieck topos of generalized functions I: basic theory [PDF]
Dissertationes Mathematicae, 2021 The main aim of the present work is to arrive at a mathematical theory close to the historically original conception of generalized functions, i.e. set theoretical functions defined on, and with values in, a suitable ring of scalars and sharing a number ...
Paolo Giordano +2 more
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General Formulation of Topos Many-Node Theory [PDF]
, 2022 We consider the created entities (events) in the first moments of universe creation. It is assumed that there exists a causal energetic relationship between all events (nodes) such that all nodes are placed on a world line and each node occupies a region
H. Simchi
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The Sierpinski Object in the Scott Realizability Topos [PDF]
Logical Methods in Computer Science, 2020 We study the Sierpinski object $\Sigma$ in the realizability topos based on Scott's graph model of the $\lambda$-calculus. Our starting observation is that the object of realizers in this topos is the exponential $\Sigma ^N$, where $N$ is the natural ...
Tom de Jong, Jaap van Oosten
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Gelfand spectra in Grothendieck toposes using geometric mathematics [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra, A, a topos T(A) of sheaves on a locale and a commutative C*-algebra, a, within that topos.
Bas Spitters +2 more
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Point-free Construction of Real Exponentiation [PDF]
Logical Methods in Computer Science, 2022 We define a point-free construction of real exponentiation and logarithms, i.e.\ we construct the maps $\exp\colon (0, \infty)\times \mathbb{R} \rightarrow \!(0,\infty),\, (x, \zeta) \mapsto x^\zeta$ and $\log\colon (1,\infty)\times (0, \infty ...
Ming Ng, Steven Vickers
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