Differential categories

@article{Blute2006DifferentialC,
  title={Differential categories},
  author={Richard Blute and J. Robin B. Cockett and Robert A. G. Seely},
  journal={Mathematical Structures in Computer Science},
  year={2006},
  volume={16},
  pages={1049 - 1083}
}
Following work of Ehrhard and Regnier, we introduce the notion of a differential category: an additive symmetric monoidal category with a comonad (a ‘coalgebra modality’) and a differential combinator satisfying a number of coherence conditions. In such a category one should imagine the morphisms in the base category as being linear maps and the morphisms in the coKleisli category as being smooth (infinitely differentiable). Although such categories do not necessarily arise from models of… 

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