Implication Details

Assumptions: one-way, zero morphisms

Conclusions: thin

Proof: If $f,g : A \rightrightarrows B$ are two morphisms, then since $0_{B,B} = \id_B$ we have $f = 0_{B,B} \circ f = 0_{A,B} = 0_{B,B} \circ g = g.$

Show 19 categories using this implication

category of abelian groups
category of finitely generated abelian groups
category of Banach spaces with linear contractions
category of commutative monoids
category of finite abelian groups
category of finite groups
category of groups
category of countable groups
category of monoids
category of left modules over a ring
category of left modules over a division ring
category of rngs
category of pointed sets
category of abelian sheaves
category of pointed topological spaces
category of torsion abelian groups
category of torsion-free abelian groups
category of vector spaces
walking idempotent