Results 1 to 10 of about 3,998 (234)
A (Discrete) Homotopy Theory for Geometric Spaces [PDF]
Journal of Mathematics, 2023 We define the concepts of homotopy and fundamental group for geometric spaces as a generalization of metric spaces, digital spaces, and graphs; then, we compare them with corresponding concepts in these spaces.
Asieh Pourhaghani, Hamid Torabi
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Torus actions, Morse homology, and the Hilbert scheme of points on affine space [PDF]
Épijournal de Géométrie Algébrique, 2021 We formulate a conjecture on actions of the multiplicative group in motivic homotopy theory. In short, if the multiplicative group G_m acts on a quasi-projective scheme U such that U is attracted as t approaches 0 in G_m to a closed subset Y in U, then ...
Burt Totaro
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Digital homotopy relations and digital homology theories
Applied General Topology, 2021 In this paper we prove results relating to two homotopy relations and four homology theories developed in the topology of digital images. We introduce a new type of homotopy relation for digitally continuous functions which we call ``strong homotopy ...
P. Christopher Staecker
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Algebraic Models of Cubical Weak Higher Structures [PDF]
Categories and General Algebraic Structures with Applications, 2022 In this article we recast some of the results developped in articles [19, 22] but in the setup of cubical geometry. Thus we define a monad on ℂ𝕊ets whose algebras are models of cubical weak ∞-groupoids with connections. In addition, we define a monad on
Camell Kachour
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Motives and homotopy theory in logarithmic geometry
Comptes Rendus. Mathématique, 2022 This document is a short user’s guide to the theory of motives and homotopy theory in the setting of logarithmic geometry. We review some of the basic ideas and results in relation to other works on motives with modulus, motivic homotopy theory, and ...
Binda, Federico +2 more
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Modalities in homotopy type theory [PDF]
Logical Methods in Computer Science, 2020 Univalent homotopy type theory (HoTT) may be seen as a language for the category of $\infty$-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes.
Egbert Rijke +2 more
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Homotopy probability theory I [PDF]
Journal of Homotopy and Related Structures, 2013 9 pages, 2 figures ...
Drummond-Cole, G, Park, JS, Terilla, J
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Canonicity and homotopy canonicity for cubical type theory [PDF]
Logical Methods in Computer Science, 2022 Cubical type theory provides a constructive justification of homotopy type theory. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices.
Thierry Coquand +2 more
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Quantum Gauge Field Theory in Cohesive Homotopy Type Theory [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We implement in the formal language of homotopy type theory a new set of axioms called cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in quantum gauge field theory.
Urs Schreiber, Michael Shulman
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2-adjoint equivalences in homotopy type theory [PDF]
Logical Methods in Computer Science, 2021 We introduce the notion of (half) 2-adjoint equivalences in Homotopy Type Theory and prove their expected properties. We formalized these results in the Lean Theorem Prover.
Daniel Carranza +3 more
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