isomorphism
Isomorphism
2010-11-01 01:41:16
2010-11-01 01:47:36
Definition
isomorphism
inverse morphism
section
retraction
mobomorphism
epimorphism
isomorphic objects under an isomorphism
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\textbf{Definition 0.1}
\bigbreak
A morphism $f: A \to B$ in a category \textbf{$C$} is an \emph{isomorphism} when there exists an \emph{inverse morphism} of $f$ in \textbf{$C$}, denoted by $\inv f: B \to A$, such that $f \circ \inv f =id_A$.
One also writes: $A \cong B$, expressing the fact that the object A is isomorphic with object B under the isomorphism $f$.