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Littérature scientifique sur le sujet « Infinity-topos »

Auteur : Grafiati

Publié le 2 juin 2025

Mis à jour le 31 juillet 2025

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Articles de revues sur le sujet "Infinity-topos"

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MCLARTY, COLIN. "THE LARGE STRUCTURES OF GROTHENDIECK FOUNDED ON FINITE-ORDER ARITHMETIC." Review of Symbolic Logic 13, no. 2 (2019): 296–325. http://dx.doi.org/10.1017/s1755020319000340.

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AbstractThe large-structure tools of cohomology including toposes and derived categories stay close to arithmetic in practice, yet published foundations for them go beyond ZFC in logical strength. We reduce the gap by founding all the theorems of Grothendieck’s SGA, plus derived categories, at the level of Finite-Order Arithmetic, far below ZFC. This is the weakest possible foundation for the large-structure tools because one elementary topos of sets with infinity is already this strong.

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McLarty, Colin. "Axiomatizing a category of categories." Journal of Symbolic Logic 56, no. 4 (1991): 1243–60. http://dx.doi.org/10.2307/2275472.

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AbstractElementary axioms describe a category of categories. Theorems of category theory follow, including some on adjunctions and triples. A new result is that associativity of composition in categories follows from cartesian closedness of the category of categories. The axioms plus an axiom of infinity are consistent iff the axioms for a well-pointed topos with separation axiom and natural numbers are. The theory is not finitely axiomatizable. Each axiom is independent of the others. Further independence and definability results are proved. Relations between categories and sets, the latter d

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Swan, Andrew W. "On the Nielsen-Schreier Theorem in Homotopy Type Theory." Logical Methods in Computer Science Volume 18, Issue 1 (January 20, 2022). http://dx.doi.org/10.46298/lmcs-18(1:18)2022.

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We give a formulation of the Nielsen-Schreier theorem (subgroups of free groups are free) in homotopy type theory using the presentation of groups as pointed connected 1-truncated types. We show the special case of finite index subgroups holds constructively and the full theorem follows from the axiom of choice. We give an example of a boolean infinity topos where our formulation of the theorem does not hold and show a stronger "untruncated" version of the theorem is provably false in homotopy type theory.

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Emmerson, Parker. "Anterolateral Lite 2." Journal of Liberated Mathematics, May 25, 2025. https://doi.org/10.5281/zenodo.15510371.

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The \emph{Anterolateral Lite 2} formalism arises from a need to robustly track analytic and symbolic distinctions that are often lost in traditional algebraic and geometric frameworks, especially in contexts involving multi-branched solutions and subtle phase phenomena, such as Lorentzian and radical expressions. Classical algebraic structures, which treat coordinates as atomic or globally coherent entities, are prone to \emph{branch collapse}: the unwanted identification of distinct solution branches through singularities, degenerate loci, or insufficiently expressive type systems. Building o

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D'Aloia, Alessandro. "Paraliminal Conceptuality and the Abstract of Infinity, or Film Philosophy into LLMs Will Do Fine." M/C Journal 27, no. 5 (2024). http://dx.doi.org/10.5204/mcj.3098.

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This article questions whether there exists a difference between the actuality and the virtuality of land as a means of image or scapeness with regard to Ben Koder’s Looking Glass Quilt and John Power’s work on generative ambient screens in public spaces as encounters. It also challenges, but more along the lines of plays with, Jeff Malpas’s contestation of space as a concept that is central to the notion of geographical thinking in the absence of a geography, but with an emphasis on the relational view of space that has come to dominate geography and the social sciences as an elucidation of s

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Thèses sur le sujet "Infinity-topos"

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Lejay, Damien. "Algèbres à factorisation et Topos supérieurs exponentiables." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066191.

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Cette these est composee de deux parties independantes ayant pour point commun l’utilisation intensive de la theorie des ∞-categories. Dans la premiere, on s’interesse aux liens entre deux approches differentes de la formalisation de la physique des particules : les algebres vertex et les algebres a factorisation a la Costello. On montre en particulier que dans le cas des theories dites topologiques, elles sont equivalentes. Plus precisement, on montre que les∞-categories de fibres vectoriels factorisant non-unitaires sur une variete algebrique complexe lisse X est equivalente a l’∞-categorie

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Bár, Filip. "Infinitesimal models of algebraic theories." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/267026.

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Smooth manifolds have been always understood intuitively as spaces that are infinitesimally linear at each point, and thus infinitesimally affine when forgetting about the base point. The aim of this thesis is to develop a general theory of infinitesimal models of algebraic theories that provides us with a formalisation of these notions, and which is in accordance with the intuition when applied in the context of Synthetic Differential Geometry. This allows us to study well-known geometric structures and concepts from the viewpoint of infinitesimal geometric algebra. Infinitesimal models of al

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