Category: Rel

Rel is the category whose objects are sets and arrows are relations.

Facts Derived from Enrichment

Rel is a 2-poset, a locally posetal or 2-thin 2-category (enriched in Pos).

Notable Subcategories

• Pfn (essentially wide)
• Rel (contravariant equivalence)
• SymmRel (core)

Limits

Colimits

categories: Rel

This data as json

Links from other tables

• 0 rows from internal_commutative_monoids in categories_of_commutative_monoids
• 0 rows from parent in categories_of_commutative_monoids
• 0 rows from completion in karoubi_envelopes
• 0 rows from category in karoubi_envelopes
• 0 rows from internal_semigroups in categories_of_semigroups
• 0 rows from parent in categories_of_semigroups
• 2 rows from category in enrichments
• 0 rows from homs in enrichments
• 1 row from internal_relations in bicategories_of_relations
• 0 rows from parent in bicategories_of_relations
• 0 rows from category in categorical_structure
• 0 rows from subcategory in subcategories
• 0 rows from parent in subcategories
• 0 rows from groupoid in cores
• 1 row from category in cores
• 0 rows from internal_monoids in categories_of_monoids
• 0 rows from parent in categories_of_monoids
• 0 rows from internal_rings in categories_of_rings
• 0 rows from parent in categories_of_rings
• 0 rows from skeleton in skeletons
• 0 rows from category in skeletons
• 0 rows from partial_category in restriction_categories
• 0 rows from total_subcategory in restriction_categories
• 0 rows from category in topoi
• 0 rows from category in monoidal_categories
• 0 rows from supercategory in full_subcategories
• 0 rows from subcategory in full_subcategories
• 1 row from supercategory in essentially_wide_subcategories
• 0 rows from subcategory in essentially_wide_subcategories
• 0 rows from category in disconnected_categories
• 0 rows from pointed in maybe_monads
• 0 rows from base in maybe_monads
• 0 rows from monoids in list_monads
• 0 rows from base in list_monads
• 0 rows from multisets in multiset_monads
• 0 rows from base in multiset_monads
• 0 rows from parent in categories_of_lie_algebras
• 0 rows from internal_lie_algebras in categories_of_lie_algebras
• 0 rows from parent in categories_of_abelian_groups
• 0 rows from internal_abelian_groups in categories_of_abelian_groups
• 0 rows from parent in categories_of_simplicial_objects
• 0 rows from internal_simplicial_sets in categories_of_simplicial_objects
• 0 rows from category in categories_with_animal_names
• 0 rows from internal_groups in categories_of_groups
• 0 rows from parent in categories_of_groups
• 0 rows from supercategory in reflective_subcategories
• 0 rows from subcategory in reflective_subcategories
• 0 rows from horizontal_2cat in double_categories
• 1 row from vertical_2cat in double_categories
• 0 rows from example_categeory in logical_completeness
• 0 rows from complete_2category in logical_completeness
• 0 rows from category in arrow_categories
• 0 rows from arrows in arrow_categories
• 1 row from op in opposite_categories
• 1 row from category in opposite_categories
• 1 row from category in dagger_categories
• 1 row from name in 2-categories