CatDat

Implication Details

Claim: If a category is one-way and has zero morphisms, then it is thin.

Proof: If f,g:ABf,g : A \rightrightarrows B are two morphisms, then since 0B,B=idB0_{B,B} = \id_B we have f=0B,Bf=0A,B=0B,Bg=g.f = 0_{B,B} \circ f = 0_{A,B} = 0_{B,B} \circ g = g.

Show 23 categories using this implication