Results 11 to 20 of about 3,998 (234)
Dolbeault homotopy theory [PDF]
Transactions of the American Mathematical Society, 1978 For complex manifolds, we define “complex homotopy groups” in terms of the Dolbeault complex. Many theorems of classical homotopy theory are reflected in the properties of complex homotopy groups. Analytic fibre bundles yield long exact sequences of complex homotopy groups and various Hurewicz theorems relate complex homotopy groups to the Dolbeault ...
Neisendorfer, Joseph, Taylor, Laurence
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On the Nielsen-Schreier Theorem in Homotopy Type Theory [PDF]
Logical Methods in Computer Science, 2022 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.
Andrew W Swan
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Correspondences and stable homotopy theory
Transactions of the London Mathematical Society, 2023 A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra SH is recovered from modules over a commutative symmetric ring ...
Grigory Garkusha
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European Physical Journal C: Particles and Fields, 2023 A new concept of moderate non-locality in higher-spin gauge theory is introduced. Based on the recently proposed differential homotopy approach, a moderately non-local scheme, that is softer than those resulting from the shifted homotopy approach ...
O. A. Gelfond
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Cellular Cohomology in Homotopy Type Theory [PDF]
Logical Methods in Computer Science, 2020 We present a development of cellular cohomology in homotopy type theory. Cohomology associates to each space a sequence of abelian groups capturing part of its structure, and has the advantage over homotopy groups in that these abelian groups of many ...
Ulrik Buchholtz, Kuen-Bang Hou
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Algebraic Models of Cubical Weak ∞-Categories with Connections [PDF]
Categories and General Algebraic Structures with Applications, 2022 In this article we adapt some aspects of Penon’s article [23] to cubical geometry. More precisely we define a monad on the category CSets of cubical sets (without degeneracies) whose algebras are models of cubical weak ∞-categories with connections.
Camell Kachour
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Lawvere-Tierney sheafification in Homotopy Type Theory
Journal of Formalized Reasoning, 2016 Sheafification is a popular tool in topos theory which allows to extend the internal logic of a topos with new principles. One of its most famous applications is the possibility to transform a topos into a boolean topos using the dense topology, which ...
Kevin Quirin, Nicolas Tabareau
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GLOBAL ACTIONS AND VECTOR $K$-THEORY
Forum of Mathematics, Sigma, 2020 Purely algebraic objects like abstract groups, coset spaces, and G-modules do not have a notion of hole as do analytical and topological objects. However, equipping an algebraic object with a global action reveals holes in it and thanks to the homotopy ...
ANTHONY BAK, ANURADHA S. GARGE
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On Relative Homotopy Groups of Modules
International Journal of Mathematics and Mathematical Sciences, 2007 In his book “Homotopy Theory and Duality,” Peter Hilton described the concepts of relative homotopy theory in module theory. We study in this paper the possibility of parallel concepts of fibration and cofibration in module theory, analogous to the ...
C. Joanna Su
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Some examples of nontrivial homotopy groups of modules
International Journal of Mathematics and Mathematical Sciences, 2001 The concept of the homotopy theory of modules was discovered by Peter Hilton as a result of his trip in 1955 to Warsaw, Poland, to work with Karol Borsuk, and to Zurich, Switzerland, to work with Beno Eckmann.
C. Joanna Su
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