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A category with a tensor product, unit object, and coherent associativity and unit isomorphisms.
wp-monoidal-categorynlab-monoidal-categoryriehl-category-contextEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Add a tensor bifunctor, unit object, associator, and unitors satisfying coherence.
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.
nlab-monoidal-categoryriehl-category-contextEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Add a natural exchange isomorphism satisfying the hexagon laws.
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.
wp-braided-categoryriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Choose internal objects giving tensor–hom adjunctions.
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.
wp-closed-monoidalnlab-closed-monoidalriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the monoidal category in which hom-objects and composition live.
Feed several structures into a construction junction and impose compatibility between them.
wp-enriched-categorynlab-enriched-categoryriehl-category-context