Implication details
Claim: A category is multi-algebraic if and only if it is a generalized variety and is multi-cocomplete.
Proof: This follows from one of the equivalent formulations of multi-algebraic categories.
Show 85 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of abelian groups
- category of large families of abelian groups
- category of finitely generated abelian groups
- category of algebras
- category of finite sets and bijections
- delooping of a group
- delooping of an infinite countable group
- delooping of a non-trivial finite group
- delooping of an infinite uncountable group
- delooping of the additive monoid of ordinal numbers
- category of sets equipped with a binary relation
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a reflexive binary relation
- category of sets equipped with a symmetric binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of coproducts of Euclidean spaces
- category of F(I)-sets
- category of finite sets and surjections
- category of filtered vector spaces
- category of finite abelian groups
- category of finite groups
- category of finite sets of even cardinality
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of fields
- category of fields of characteristic zero
- category of free abelian groups
- category of finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of finitely generated groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of monoids
- category of sets with a distinguished subset
- partially ordered set of extended natural numbers
- category of partially ordered sets without isolated points
- category of quivers
- category of quivers with finite components
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of sets and relations
- category of rings
- category of rngs
- category of semigroups
- category of sequences of sets
- category of connected sequences of sets
- category of sets
- category of pointed sets
- category of set functions and commutative squares
- category of sets and bijections
- discrete category of sets
- category of large families of sets
- category of large families of sets and bijections
- category of large families of sets which are mostly singletons
- category of sets with finite-to-one maps
- indiscrete category of sets
- category of pairs of sets
- category of empty-or-finite pairs of sets
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of vector spaces
- category of large families of vector spaces which are mostly zero
- category of Z-functors
- category of finite Z-sets
- category of Z-sets
- category of ω-sets
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking fork
- walking idempotent
- walking isomorphism
- walking morphism
- walking parallel pair
- walking span
- walking splitting