一句话：证明 codereliction 即使定义在非加法环境中也会通过双代数卷积诱导加法富集，并刻画微分线性范畴和唯一性。
微分线性范畴为微分线性逻辑的乘法与指数片段提供范畴语义，它是对交换幺半群富集的对称幺半范畴，并带有一个装备 codereliction 的 monoidal coalgebra modality；加法富集用于表达 Leibniz 规则。本文提出：codereliction 的公理本身不涉及和与零，因此可尝试在非加法环境中定义。作者证明，即便可以如此定义，codereliction 仍会通过双代数卷积诱导出加法富集，从而得到微分线性范畴的新刻画：带 monoidal bialgebra modality 与 codereliction 的对称幺半范畴。文章还证明 codereliction 实际上唯一，并引入 monoidal Hopf coalgebra modalities，讨论 antipode 与对阿贝尔群富集的关系。
Differential linear categories provide the categorical semantics of the multiplicative and exponential fragments of Differential Linear Logic. Briefly, a differential linear category is a symmetric monoidal category that is enriched over commutative monoids (called additive enrichment) and has a monoidal coalgebra modality that is equipped with a codereliction. The codereliction is what captures the ability of differentiating non-linear proofs via linearization in Differential Linear Logic. The additive enrichment plays an important role since it allows one to express the famous Leibniz rule. However, the axioms of a codereliction can be expressed without any sums or zeros. Therefore, it is natural to ask if one can consider a possible non-additive enriched version of differential linear categories. In this paper, we show that even if a codereliction can technically be defined in a non-additive setting, it nevertheless induces an additive enrichment via bialgebra convolution. Thus, we obtain a novel characterization of a differential linear category as a symmetric monoidal category with a monoidal bialgebra modality equipped with a codereliction. Moreover, we also show that coderelictions are, in fact, unique. We also introduce monoidal Hopf coalgebra modalities and discuss how antipodes relate to enrichment over Abelian groups.