Implication Details
Assumptions: equalizers, subobject-trivial
Conclusions: thin
Proof: If are morphisms, their equalizer is a monomorphism , hence an isomorphism. But this means .
Show 48 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of algebras
- category of combinatorial species
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of countable groups
- category of countable sets
- category of fields
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of finite sets and injections
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of finitely generated abelian groups
- category of groups
- category of Jónsson-Tarski algebras
- category of left modules over a division ring
- category of left modules over a ring
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of monoids
- category of pairs of sets
- category of pointed sets
- category of pointed topological spaces
- category of posets
- category of prosets
- category of pseudo-metric spaces with non-expansive maps
- category of rings
- category of rngs
- category of semigroups
- category of sets
- category of sets with finite-to-one maps
- category of sheaves
- category of simplicial sets
- category of small categories
- category of topological spaces
- category of torsion abelian groups
- category of vector spaces
- category of Z-functors
- delooping of the additive monoid of ordinal numbers
- walking fork
- walking splitting