adjunction

Noun

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Noun

**adjunction**

- 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*en*meronyms*en

- Portuguese: adjunção

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.005