Adjunction

English

Etymology

Template:Root From Template:Lbor, from Template:M: compare Template:Cog, and see Template:M.

Pronunciation

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Noun

1. Template:Senseid The act of joining; the thing joined or added.
2. Template:Senseid Template:Lb The joining of personal property owned by one to that owned by another.
3. Template:Lb The process of adjoining elements to an algebraic structure (usually a ring or field); the result of such a process.

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4. Template:Lb A relationship between a pair of categories that makes the pair, in a weak sense, equivalent.

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5. Template:Senseid Template:Lb A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object.
   1. (formally, given two categories $𝒞$ and $𝒟$ and (covariant) functors $F:𝒞\to 𝒟$ and $G:𝒟\to 𝒞$) A natural isomorphism $\mathrm{\Phi }:{\mathrm{Hom}}_{𝒞}(G\cdot ,\cdot )\to {\mathrm{Hom}}_{𝒟}(\cdot ,F\cdot )$ (where the hom-functors are understood as bifunctors from ${𝒟}^{\mathrm{op}}\times 𝒞$ to $𝐒𝐞𝐭$). See Template:Pedia.

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Translations

• Polish: Template:T
• Portuguese: Template:T

• Polish: Template:T

• Bulgarian: Template:T+check