We construct a 2-categorical extension of the relative entropy functor of Baez and Fritz, and show that our construction is functorial with respect to vertical morphisms. Moreover, we show such a `2-relative entropy' satisfies natural 2-categorial analogues of convex linearity, vanishing under optimal hypotheses, and lower semicontinuity. While relative entropy is a relative measure of information between probability distributions, we view our construction as a relative measure of information between channels.

翻译：我们建造了Baez和Fritz的相对酶真菌配方的2类延伸,并表明我们的构造与垂直形态相对是相对的。此外,我们展示了这种“2-反应酶”符合相近线性、在最佳假设下消失和半连续性较低的自然2类类比。相对的酶是概率分布之间信息的相对量度,但我们认为我们的构造是不同频道之间信息的相对量度。