ADJUNCTION

junction, adjunction

(noun) an act of joining or adjoining things

Source: WordNet® 3.1


Etymology

Noun

adjunction (countable and uncountable, plural adjunctions)

The act of joining; the thing joined or added.

(legal) The joining of personal property owned by one to that owned by another.

(category theory) 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.

Hyponyms: equivalence of categories, isomorphism of categories, Galois connection

Meronyms: adjoint, left adjoint, right adjoint

Source: Wiktionary


Ad*junc"tion, n. Etym: [L. adjunctio, fr. adjungere: cf. F. adjonction, and see Adjunct.]

Definition: The act of joining; the thing joined or added.

Source: Webster’s Unabridged Dictionary 1913 Edition



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Word of the Day

23 May 2025

THOUGHTFULLY

(adverb) showing consideration and thoughtfulness; “he had thoughtfully brought with him some food to share”


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