# 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} }

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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