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Closed monoidal category

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Summary

A monoidal category in which tensoring has internal-hom right adjoints.

Record metadata

Carrier(s)

Data

Axioms / constraints

Concept sources

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Compact closed categoryClosed monoidal category

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

Authored explanation

Compact closure canonically supplies internal homs, for example [A,B]=AB[A,B]=A^*\otimes B, and hence a closed monoidal structure.

How to interpret this relation type

Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.

Relation sources

Monoidal categoryClosed monoidal category

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

Authored explanation

Choose internal hom\operatorname{hom} objects giving tensor–hom adjunctions.

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

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Each relation below starts at this concept.

No direct relations are authored in this direction.