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The Interval Domain in Homotopy Type Theory
Even though the real numbers are the cornerstone of many fields in mathematics, it is challenging to formalize them in a constructive setting, and in...
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Topological Quantum Gates in Homotopy Type Theory
Despite the plausible necessity of topological protection for realizing scalable quantum computers, the conceptual underpinnings of topological...
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Differential contracting homotopy in higher-spin theory
A new efficient approach to the analysis of nonlinear higher-spin equations, that treats democratically auxiliary spinor variables Z A and integration...
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The cube axiom and resolutions in homotopy theory
We show that a version of the cube axiom holds in cosimplicial unstable coalgebras and cosimplicial spaces equipped with a resolution model...
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Eilenberg–Maclane spaces and stabilisation in homotopy type theory
In this note, we study the deloo** of spaces and maps in homotopy type theory. We show that in some cases, spaces have a unique deloo**, and give...
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Random simple-homotopy theory
We implement an algorithm RSHT (random simple-homotopy) to study the simple-homotopy types of simplicial complexes, with a particular focus on...
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Mysterious Triality and Rational Homotopy Theory
Mysterious Duality has been discovered by Iqbal, Neitzke, and Vafa (Adv Theor Math Phys 5:769–808, 2002) as a convincing, yet mysterious...
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Homotopy Theory: Fundamental Group and Higher Homotopy Groups
This chapter officially inaugurates homotopy theory to begin a study of algebraic topology by conveying the basic concepts of homotopy and...
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Homotopy prefactorization algebras
We apply the theory of operadic Koszul duality to provide a cofibrant resolution of the colored operad whose algebras are prefactorization algebras...
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Weak Graph Map Homotopy and Its Applications
The authors introduce a notion of a weak graph map homotopy (they call it M -homotopy), discuss its properties and applications. They prove that the...
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Weight Decompositions on Algebraic Models for Map** Spaces and Homotopy Automorphisms
We obtain restrictions on the rational homotopy types of map** spaces and of classifying spaces of homotopy automorphisms by means of the theory of...
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A homotopy analysis solution to large deformation of a nanowire based on nonlocal elasticity theory
On the basis of Eringen’s nonlocal elasticity theory, large deflection of a cantilever nanowire under a uniformly distributed load is investigated...
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Homotopy Theory in Digital Topology
Digital topology is part of the ongoing endeavor to understand and analyze digitized images. With a view to supporting this endeavor, many notions...
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Homotopy Sheaves on Generalised Spaces
We study the homotopy right Kan extension of homotopy sheaves on a category to its free cocompletion, i.e. to its category of presheaves. Any...
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The Homotopy Type of G/TOP, G/PL and G/O
In this chapter we review how to determine the homotopy types of the spaces G/PL and G/TOP and discuss some related results. We have already seen the...