Differential categories axiomatize the basics of differentiation and provide categorical models of differential linear logic. A differential category is said to have antiderivatives if a natural transformation , which all differential categories have, is a natural isomorphism. Differential categories with antiderivatives come equipped with a canonical integration operator such that generalizations of the Fundamental Theorems of Calculus hold. In this paper, we show that Blute, Ehrhard, and Tasson's differential category of convenient vector spaces has antiderivatives. To help prove this result, we show that a differential linear category – which is a differential category with a monoidal coalgebra modality – has antiderivatives if and only if one can integrate over the monoidal unit and such that the Fundamental Theorems of Calculus hold. We also show that generalizations of the relational model (which are biproduct completions of complete semirings) are also differential linear categories with antiderivatives.

中文翻译：

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微分线性类别的方便反导数

微分范畴公理化微分的基础并提供微分线性逻辑的分类模型。如果所有微分范畴都具有的自然变换 是自然同构，则称微分范畴具有反导数。带有反导数的微分类别配备了规范积分算子，因此微积分基本定理的推广成立。在本文中，我们证明了 Blute、Ehrhard 和 Tasson 的便利向量空间微分范畴具有反导数。为了帮助证明这个结果，我们证明了一个微分线性范畴——它是一个具有幺半群代数模态的微分范畴——具有反导数当且仅当一个人可以在幺半群单元上积分并且使得微积分基本定理成立。