Unity and identity of opposites in calculus and physics

@article{Lawvere1996UnityAI,
  title={Unity and identity of opposites in calculus and physics},
  author={F. William Lawvere},
  journal={Applied Categorical Structures},
  year={1996},
  volume={4},
  pages={167-174}
}
  • F. W. Lawvere
  • Published 1 June 1996
  • Physics
  • Applied Categorical Structures
A significant fraction of dialectical philosophy can be modeled mathematically through the use of “cylinders” (diagrams of shape Δ) in a category, wherein the two identical subobjects (united by the third map in the diagram) are “opposite”. In a bicategory, oppositeness can be very effectively characterized in terms of adjointness, but even in an ordinary category it may sometimes be given a useful definition. For example, an effective basis for teaching calculus is a ringed category satisfying… 

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