adjunction
/æˈdʒʌŋkʃən/
noun
التحاق
Given a pair of categories \mathcal{C} and \mathcal{D}: an anti-parallel pair of functors F:\mathcal{C}\rightarrow \mathcal{D} and G:\mathcal{D}\rightarrow \mathcal{C} and a natural transformation \eta:\mbox{id}_C \rightarrow GF called “unit” such that for any object A \in \mathcal{C}, for any object B \in \mathcal{D}, and for any morphism f:A\rightarrow GB, there is a unique morphism g:FA\rightarrow B such that Gg \circ \eta_A = f. (Note: there is another natural transformation called “counit” as well but its existence may be derived by theorem.) The pair of functors express a similarity between the pair of categories which is weaker than that of an equivalence of categories.
شرح الأستاذ مفهوم الالتحاق بين بنيتين رياضيتين باستخدام أمثلة من نظرية الزمر والجبر الخطي، موضحًا كيف يؤسس علاقة رسمية بينهما.