Results 11 to 20 of about 1,564 (187)
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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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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A model for the homotopy theory of homotopy theory [PDF]
Transactions of the American Mathematical Society, 2000 We describe a category, the objects of which may be viewed as models for homotopy theories. We show that for such models, “functors between two homotopy theories form a homotopy theory”, or more precisely that the category of such models has a well-behaved internal hom-object.
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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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Homotopy Theory in Digital Topology [PDF]
Discrete & Computational Geometry, 2021 Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some of the most basic notions from homotopy theory remain largely absent from the digital topology literature.
Gregory Lupton +2 more
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Homotopy theory of bicomplexes [PDF]
Journal of Pure and Applied Algebra, 2019 We define two model structures on the category of bicomplexes concentrated in the right half plane. The first model structure has weak equivalences detected by the totalisation functor. The second model structure's weak equivalences are detected by the $E^2$-term of the spectral sequence associated to the filtration of the total complex by the ...
Muro Jiménez, Fernando +1 more
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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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Complex Manifolds, 2022 We give an exposition of Sullivan’s theorem on realizing rational homotopy types by closed smooth manifolds, including a discussion of the necessary rational homotopy and surgery theory, adapted to the realization problem for almost complex manifolds ...
Milivojević Aleksandar
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Algebraic Theories in Homotopy Theory [PDF]
The Annals of Mathematics, 2002 An algebraic theory $T$ is a category with objects $t_0,t_2...$ such that for each $n$ the object $t_n$ is an $n$-fold categorical product of $t_1$. A strict $T$-algebra is a product preserving functor $A: T\to Spaces$. Lawvere showed that for a suitable choice of T giving such an algebra amounts to providing the space $A(t_1)$ with a familiar ...
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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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