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A mapping between categories that sends objects to objects and morphisms to morphisms while preserving identities and composition.
wp-functornlab-functorriehl-category-contextEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Choose a target category and specify object and morphism assignments that preserve identities and composition.
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.
riehl-category-contextEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
An adjunction consists of a left and right adjoint functor together with equivalent unit/counit or hom-set data; a single functor need not possess an adjoint.
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.
riehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
A diagram is a functor into a category; when a universal cocone exists, its apex is the colimit of that diagram.
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.
riehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
A diagram is a functor into a category; when a universal cone exists, its apex is the limit of that diagram.
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.
riehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Choose a second parallel functor and supply component morphisms satisfying the naturality equations.
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.
riehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
A presheaf is a functor from the opposite of a category to Set.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
riehl-category-context