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Cartesian closed category

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Summary

A cartesian category in which product with each object has a right adjoint.

Record metadata

Carrier(s)

Data

Axioms / constraints

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Cartesian categoryCartesian closed category

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Add internal hom\operatorname{hom} objects right-adjoint to product.

How to interpret this relation type

Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Cartesian closed categoryAdjunction

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

In a cartesian closed category, for each object AA the functor ()×A(-)\times A is left adjoint to the exponential functor ()A(-)^A.

How to interpret this relation type

Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.

Relation sources

Cartesian closed categoryfinite limits + exponentials(construction junction)

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Use the cartesian-closed structure.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources