An [[Isomorphism]] is a type of [[Homomorphism]], that is a [[Morphism|structure-preserving]] [[Function|map]] $f$ between two algabraic structures of the same type $A, B$ that can be inversed through an [[Inverse Function|inverse mapping]] $f^{-1}$. $\huge \begin{align} f: A \to B \\ f(f^{-1}(x)) \mapsto x\\ \end{align} $ Two algabraic structures $A, B$ are considered [[Isomorphism|Isomorphic]] if [[Existential Quantifier|there exists]] *any* [[Isomorphism]] between the two, and is denoted as: $\huge A \cong B $ A [[Function|map]] between is [[Isomorphism|isomorphic]] [[Biconditional|if and only if]] it is [[Bijective|bijective]]. >[!warning] >This is true for the majority of cases, but I'm told that there are some [[Isomorphism|isomorphisms]] on [[Concrete Category|concrete categories]] that don't follow this rule, and are ismorphic without being bijective (ex. the category of [[Topological Space|topological spaces]]. From what I have read, this statement is true when talking about [[Category|categories]] whose objects are [[Set|sets]] and [[Morphism|morphisms]] are [[Function|functions]] that act upon [[Set|sets]].