Revisiting differential categories: new results on the foundation of differentiation

Thesis

The theory of differential categories uses category theory to provide the mathematical foundations of differentiation in both mathematics and computer science. Differential categories are successful because they capture both the classical limit definition of differentiation and the more algebraic synthetic definition of differentiation. As such, the theory of differential categories has been able to formalize various aspects of differential calculus, from the very basic foundational aspect...

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Authors: Lemay, JSP

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Commutative Algebra; Differentiation; Differential Linear Logic; Exponential Function; Coalgebra Modality; Additive Bialgebra Modality; Differential Category; Differential Calculus; Linearizing Combinator; Cartesian Differential Category; Category Theory
• Subjects: Categories (Mathematics); Mathematics