Editing Dialectic (section)

=== Mathematics ===
Mathematician [[William Lawvere]] interpreted dialectics in the setting of [[categorical logic]] in terms of [[Adjoint functors|adjunctions]] between [[Reflective subcategory|idempotent monads]].<ref>{{cite journal |last=Lawvere |first=F. William |author-link=William Lawvere |title=Unity and identity of opposites in calculus and physics |journal=Applied Categorical Structures |date=1996 |volume=4 |issue=2–3 |pages=167–174 |doi=10.1007/BF00122250 |s2cid=34109341}}</ref> This perspective may be useful in the context of [[theoretical computer science]] where the duality between [[Syntax (programming languages)|syntax]] and [[Semantics (computer science)|semantics]] can be interpreted as a dialectic in this sense. For example, the [[Curry–Howard correspondence]] is such an adjunction or more generally the duality between [[closed monoidal categories]] and their [[internal logic]].<ref>{{cite book |last1=Eilenberg |first1=Samuel |last2=Kelly |first2=G. Max |chapter=Closed Categories |title=Proceedings of the Conference on Categorical Algebra |date=1966 |pages=421–562 |doi=10.1007/978-3-642-99902-4_22 |isbn=978-3-642-99904-8 |s2cid=251105095}}</ref>