Monomorphism - Revision history

Vipul: New page: ==Definition== ===Definition with symbols=== Suppose $\mathcal{C}$ is a category, $A,B \in \operatorname{Ob}\mathcal{C}$ , and $f \in \mathcal{C}(A,B)$
2008-12-09T00:50:39Z

New page: ==Definition== ===Definition with symbols=== Suppose <math>\mathcal{C}</math> is a category, <math>A,B \in \operatorname{Ob}\mathcal{C}</math>, and <math>f \in \mathcal{C}(A,B)</math...

New page
==Definition==

===Definition with symbols===

Suppose <math>\mathcal{C}</math> is a [[category]], <math>A,B \in \operatorname{Ob}\mathcal{C}</math>, and <math>f \in \mathcal{C}(A,B)</math>. We say that <math>f</math> is '''monic''', or is a '''monomorphism''', if for any object <math>C</math> and any <math>g,h \in \mathcal{C}(C,A)</math>, we have:

<math>f \circ g = f \circ h \implies g = h</math>.

In other words, the morphism is left-cancellative.

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Isomorphism]]
* [[Weaker than::Section]]

===Related properties===

* [[Epimorphism]]