Diffeological principal bundles and principal infinity bundles

DOI10.1007/s40062-024-00347-4zbMATH Open1547.55007MaRDI QIDQ6541388

Emilio Minichiello

Publication date: 17 May 2024

Published in: Journal of Homotopy and Related Structures (Search for Journal in Brave)

zbMATH Keywords

diffeological spacessimplicial presheavesCartesian spacesgood open covers

Mathematics Subject Classification ID

Global differential geometry (53C99) Differentiable manifolds, foundations (58A05) Generalizations of fiber spaces and bundles in algebraic topology (55R65) Other homology theories in algebraic topology (55N35) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Fiber bundles in algebraic topology (55R10) Differential spaces (58A40)

Cites Work

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• Principal \(\infty \)-bundles: general theory
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• The diffeology of Milnor's classifying space
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• Smooth classifying spaces
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• Homotopy limits, completions and localizations
• D\'ecalage and Kan's simplicial loop group functor
• Internal categories, anafunctors and localisations
• Categorical Homotopy Theory
• Convenient categories of smooth spaces
• COSIMPLICIAL SPACES AND COCYCLES
• Hypercovers and simplicial presheaves
• Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps
• Higher Topos Theory (AM-170)
• Tangent spaces and tangent bundles for diffeological spaces
• On the van Kampen theorem
• Universal homotopy theories
• Principal \(\infty\)-bundles and smooth string group models
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