Sanan adjunction käännös englanti-
Sanan adjunction määritelmät
- The act of joining; the thing joined or added
- Given a pair of categories and : an anti-parallel pair of functors and and a natural transformation called “unit” such that for any object , for any object , and for any morphism , there is a unique morphism such that .
The pair of functors express a similarity between the pair of categories which is weaker than that of an equivalence of categories
Esimerkit
- Example of an adjunction: this is from propositional logic. Consider a “logical theory” category whose objects are well-formed propositional formulae and whose arrows are logical entailment. (Entailment is a pre-ordering; and prosets qualify as a type of category.) Consider the contravariant endofunctor (negation) which when applied to a formula yields its negation , and which when applied to an entailment yields its contrapositive . Then is adjoint to itself, i.e. it is self-adjoint: , because . This is true both in classical logic and in intuitionistic logic. However, in classical logic it is also true that , so that is self-inverse (up to isomorphism), which means that is classically a self-equivalence of the “theory” category; this is stronger than the intuitionistic self-adjunction of the said theory.--