Difference between revisions of "Template:Category theory navbox"

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(Created page with "{{Navbox |name=Category theory navbox |style= border: 1px solid #aaa;width: 100%;margin: auto;clear: both;font-size: 88%;text-align: center;padding: 1px; background: #fdfdfd;...")
 
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|name=Category theory navbox
 
|name=Category theory navbox
 
|style=  border: 1px solid #aaa;width: 100%;margin: auto;clear: both;font-size: 88%;text-align: center;padding: 1px; background: #fdfdfd;
 
|style=  border: 1px solid #aaa;width: 100%;margin: auto;clear: both;font-size: 88%;text-align: center;padding: 1px; background: #fdfdfd;
 +
|state=plain
 
|groupstyle=  white-space: nowrap;  text-align: right;  font-weight: bold;  padding-left: 1em;  padding-right: 1em;background: #ddddff;  
 
|groupstyle=  white-space: nowrap;  text-align: right;  font-weight: bold;  padding-left: 1em;  padding-right: 1em;background: #ddddff;  
 
|liststyle=border-color: #fdfdfd;
 
|liststyle=border-color: #fdfdfd;
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|abovestyle=background: #ddddff;
 
|abovestyle=background: #ddddff;
 
|title=Category Theory
 
|title=Category Theory
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|above=Overview of the concepts of [[Category theory (subject)|Category Theory]]
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|above=Overview of the concepts of [[Category Theory (subject)|Category Theory]]
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|image=<span style="font-size:0.7em;">{{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] } }}</span>
+
|image=<div style="font-size:0.65em;overflow:hidden;">{{:Types of category arrows/Diagram}}</div>
 
|group1=Key objects
 
|group1=Key objects
 
|list1=[[Category]], [[Functor]] ([[Covariant functor|Covariant]], [[Contravariant functor|Contravariant]]), [[Subcategory]]
 
|list1=[[Category]], [[Functor]] ([[Covariant functor|Covariant]], [[Contravariant functor|Contravariant]]), [[Subcategory]]
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|group2=Typical [[morphism]] types<br/><span style="font-weight:normal;">(see diagram on right)</span>
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|group2=[[Types of category arrows|Typical morphism types]]<br/><span style="font-weight:normal;">(see diagram on right)</span>
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|list2=[[Arrow]] ({{AKA}}: [[Morphism]]), [[Monic]], [[Epic]], [[Bimorphism]], [[Split monic]] ({{AKA}}: [[section (category theory)|Section]]), [[Split epic]] ({{AKA}}: [[retraction (category theory)|Retraction]]), [[Isomorphism]]
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|list2=[[Arrow]] ({{AKA}}: [[Morphism]]), [[Monic]], [[Epic]], [[Bimorphism]], [[section (category theory)|Section]] ({{AKA}}: [[Split monic]]), [[retraction (category theory)|Retraction]] ({{AKA}}: [[Split epic]]), [[Isomorphism (category theory)|Isomorphism]]
 
|group3=Key objects
 
|group3=Key objects
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|list3=[[Initial (category theory)|{{M|\text{Initial} }}]], [[Final (category theory)|{{M|\text{Final} }}]]
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|list3=[[Initial (category theory)|{{M|\text{Initial} }}]], [[Final (category theory)|{{M|\text{Final} }}]] ([[initial and final compared (category theory)|compared]])
−
|group4=Key constructs
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|group4=Primitive constructs
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|list4=[[product (category theory)|Product]] / [[coproduct (category theory)|Coproduct]], [[Limit (category theory)|Limit]] / [[Colimit (category theory)|Colimit]], [[Equaliser (category theory)|Equaliser]] / [[Coequaliser (category theory)|Coequaliser]]
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|list4=[[Wedge (category theory)|Wedge]] ({{AKA}} [[Cone (category theory)|Cone]] & [[cocone (category theory)|Cocone]])
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|group5=Important examples
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|group5=Key constructs
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|list5=<nowiki/>
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|list5=[[product (category theory)|Product]] / [[coproduct (category theory)|Coproduct]] ([[Product and coproduct compared]]), [[Limit (category theory)|Limit]] / [[Colimit (category theory)|Colimit]], [[Equaliser (category theory)|Equaliser]] / [[Coequaliser (category theory)|Coequaliser]]
 +
|group6=Important examples
 +
|list6=<nowiki/>
 
* [[Demonstrating why category arrows are best thought of as arrows and not functions]]
 
* [[Demonstrating why category arrows are best thought of as arrows and not functions]]
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|group6=Trivial category examples
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|group7=Trivial category examples
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|list6=[[Category induced by a monoid]], [[Category induced by a poset]]
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|list7=[[Category induced by a monoid]], [[Category induced by a poset]]
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|group7=Common categories
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|group8=Common categories
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|list7=[[SET]], [[Pfn]], [[GROUP]]
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|list8=[[SET (category)|{{M|\mathrm{SET} }}]], [[Pfn (category)|{{M|\mathrm{Pfn} }}]], [[GROUP (category)|{{M|\mathrm{GROUP} }}]]
 
}}<noinclude>
 
}}<noinclude>
 
[[Category:Navboxes]]
 
[[Category:Navboxes]]
 
[[Category:Category Theory]]
 
[[Category:Category Theory]]
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{{Todo|fill this out}}
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{{ProjectTodo|Navbox project|fill this out}}
−
{{Todo|Can diagram be any neater?}}
+
 
</noinclude>
 
</noinclude>

Latest revision as of 20:26, 15 November 2016

v • d • e
 
Category Theory
Overview of the concepts of Category Theory
Key objects
[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]
Typical morphism types
(see diagram on right)
Key objects
Primitive constructs
Key constructs
Important examples
Trivial category examples
Common categories
Todo (Navbox project): fill this out
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