adjunction
/æˈdʒʌŋkʃən/
noun
noun
संलग्नता
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.
प्रोफेसर ने समूह सिद्धांत और रैखिक बीजगणित के उदाहरणों का उपयोग करते हुए दो गणितीय संरचनाओं के बीच संलग्नता की अवधारणा को समझाया, यह दिखाते हुए कि यह उनके बीच एक औपचारिक संबंध कैसे स्थापित करता है।