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



RESET




Word of the Day

6 January 2025

PREMATURELY

(adverb) (of childbirth) before the end of the normal period of gestation; “the child was born prematurely”


coffee icon

Coffee Trivia

Contrary to popular belief, coffee beans are not technically beans. They are referred to as such because of their resemblance to legumes. A coffee bean is a seed of the Coffea plant and the source for coffee. It is the pit inside the red or purple fruit, often referred to as a cherry. Just like ordinary cherries, the coffee fruit is also a so-called stone fruit.

coffee icon