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A collection of objects labelled by elements of an index set.
wp-indexed-familyopenlogic-set-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
An indexed family is a function whose domain is treated as an index set.
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
wp-indexed-familyopenlogic-set-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Identify or replace the index set by a product of degree sets, usually .
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.
stacks-graded-objectsThis is an authored directed relation from the source endpoint to the target endpoint.
Identify or replace the index set by a degree set, usually or .
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.
stacks-graded-objectsThis is an authored directed relation from the source endpoint to the target endpoint.
For a family of subsets of a vertex set, take its image in the power set. This forgets the index labels and repeated hyperedges, so the construction is not invertible in general.
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.
mathlib-hypergraphThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the family of objects indexed by nonnegative degrees.
Feed several structures into a construction junction and impose compatibility between them.
stacks-simplicial-objectsnlab-simplicial-objectwp-cosimplicial-objectriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Supply a family indexed by an ordered time set.
Feed several structures into a construction junction and impose compatibility between them.
wp-filtration-probabilitydurrett-probabilityThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the family of objects indexed by nonnegative degrees.
Feed several structures into a construction junction and impose compatibility between them.
stacks-simplicial-objectsnlab-simplicial-objectriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the Indexed family structure as one jointly required input.
Feed several structures into a construction junction and impose compatibility between them.
wp-stochastic-processdurrett-probability