Differential structure, tangent structure, and SDG

DOI10.1007/s10485-013-9312-0zbMath1304.18031OpenAlexW2108070223MaRDI QIDQ2015833

G. S. H. Cruttwell, J. Robin B. Cockett

Publication date: 24 June 2014

Published in: Applied Categorical Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10485-013-9312-0

zbMATH Keywords

synthetic differential geometryCartesian differential categorytangent structure

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Synthetic differential geometry (51K10) Abstract manifolds and fiber bundles (category-theoretic aspects) (18F15)

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Cites Work

• Unnamed Item
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• Unnamed Item
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• Unnamed Item
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• Unnamed Item
• Unnamed Item
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• Unnamed Item
• The differential lambda-calculus
• Skew-closed categories
• Differential restriction categories
• Closed categories vs. closed multicategories
• Euler’s Continuum Functorially Vindicated
• Categorical Models for Simply Typed Resource Calculi
• On Köthe sequence spaces and linear logic
• Axiomatic Differential Geometry II-1 Vector Fields
• Restriction categories III: colimits, partial limits and extensivity
• Restriction categories. I: Categories of partial maps

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