Difference between revisions of "Types of category arrows/Diagram"
From Maths
(Created page with "<noinclude> ==Diagram showing how terms for arrows in a category relate== References: <br/><br/> </noinclude>{{M|1=\xymatrix{ & \text{Arrow} \\ \text{Monic} \ar@{^{(}->}[ur] &...") |
m |
||
Line 3: | Line 3: | ||
References: | References: | ||
<br/><br/> | <br/><br/> | ||
− | </noinclude>{{M|1=\xymatrix{ & \text{Arrow} \\ \text{Monic} \ar@{^{(}->}[ur] & & \text{Epic} \ar@{^{(}->}[ul] \\ & \text{Bimorphism} \ar@{^{(}->}[ur] \ar@<-0.5ex>@{^{(}->}[ul] \\ \text{Split monic} \ar@{^{(}->}[uu] & & \text{Split epic} \ar@<-0.75ex>@{^{(}->}[uu] \\ & \text{Isomorphism} \ar@{^{(}->}[ur] \ar@<-0.5ex>@{^{(}->}[ul] \ar@{^{(}->}[uu] } }}<noinclude> | + | </noinclude>{{M|1=\xymatrix{ & \text{Arrow} \\ \text{Monic} \ar@{^{(}->}[ur] & & \text{Epic} \ar@{^{(}->}[ul] \\ & \text{Bimorphism} \ar@{^{(}->}[ur] \ar@<-0.5ex>@{^{(}->}[ul] \\ {\begin{array}{c}\text{Section}\\ \text{(Split monic)} \end{array} } \ar@{^{(}->}[uu] & & {\begin{array}{c}\text{Retraction}\\ \text{(Split epic)} \end{array} } \ar@<-0.75ex>@{^{(}->}[uu] \\ & \text{Isomorphism} \ar@{^{(}->}[ur] \ar@<-0.5ex>@{^{(}->}[ul] \ar@{^{(}->}[uu] } }}<noinclude> |
{{Todo|Can diagram be any neater?}} | {{Todo|Can diagram be any neater?}} | ||
[[Category:Diagrams showing how things relate]] | [[Category:Diagrams showing how things relate]] |
Latest revision as of 14:50, 6 February 2016
Diagram showing how terms for arrows in a category relate
References:
[ilmath]\xymatrix{ & \text{Arrow} \\ \text{Monic} \ar@{^{(}->}[ur] & & \text{Epic} \ar@{^{(}->}[ul] \\ & \text{Bimorphism} \ar@{^{(}->}[ur] \ar@<-0.5ex>@{^{(}->}[ul] \\ {\begin{array}{c}\text{Section}\\ \text{(Split monic)} \end{array} } \ar@{^{(}->}[uu] & & {\begin{array}{c}\text{Retraction}\\ \text{(Split epic)} \end{array} } \ar@<-0.75ex>@{^{(}->}[uu] \\ & \text{Isomorphism} \ar@{^{(}->}[ur] \ar@<-0.5ex>@{^{(}->}[ul] \ar@{^{(}->}[uu] }[/ilmath]
TODO: Can diagram be any neater?
TODO: References
References