[{"word":"adjunction","phonetics":[],"meanings":[{"partOfSpeech":"noun","definitions":[{"definition":"The act of joining; the thing joined or added.","synonyms":[],"antonyms":[]},{"definition":"The joining of personal property owned by one to that owned by another.","synonyms":[],"antonyms":[]},{"definition":"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.","synonyms":[],"antonyms":[]}],"synonyms":[],"antonyms":[]}],"license":{"name":"CC BY-SA 3.0","url":"https://creativecommons.org/licenses/by-sa/3.0"},"sourceUrls":["https://en.wiktionary.org/wiki/adjunction"]}]