Isomorphism

Collection

context $A,B\in\mathrm{Ob}_{\bf C}$
definiendum $f$ in $A\cong B$
inclusion $f:{\bf C}[A,B]$
exists $f^{-1}:{\bf C}[B,A]$
postulate $f^{-1}\circ f=\mathrm{id}_A$
postulate $f\circ f^{-1}=\mathrm{id}_B$

Reference

Wikipedia: Isomorphism, Automorphism


Context

Categories