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A collection of objects whose homs are objects of a monoidal category, with enriched composition and units.
An underlying ordinary category exists only when the enriching base supplies an appropriate way to extract hom-sets.
wp-enriched-categorynlab-enriched-categoryriehl-category-contextEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Choose hom-objects, composition morphisms, and unit morphisms satisfying the enriched category axioms.
Feed several structures into a construction junction and impose compatibility between them.
wp-enriched-categorynlab-enriched-categoryriehl-category-contextEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require the enriching monoidal category to be chain complexes over a specified commutative base ring, with the chosen grading/sign convention.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-dg-categorynlab-dg-categorystacks-derived-text