Template:Category theory navbox

From Maths

Revision as of 11:44, 19 February 2016 by Alec (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Jump to: navigation, search

v • d • e Category Theory

Overview of the concepts of Category Theory

Key objects	Category, Functor (Covariant, Contravariant), Subcategory	[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)	Arrow (AKA: Morphism), Monic, Epic, Bimorphism, Section (AKA: Split monic), Retraction (AKA: Split epic), Isomorphism

Key objects	[ilmath]\text{Initial} [/ilmath], [ilmath]\text{Final} [/ilmath]

Key constructs	Product / Coproduct, Limit / Colimit, Equaliser / Coequaliser

Important examples	Demonstrating why category arrows are best thought of as arrows and not functions

Trivial category examples	Category induced by a monoid, Category induced by a poset

Common categories	[ilmath]\mathrm{SET} [/ilmath], [ilmath]\mathrm{Pfn} [/ilmath], [ilmath]\mathrm{GROUP} [/ilmath]

Todo (Navbox project): fill this out

Retrieved from "https://www.maths.kisogo.com/index.php?title=Template:Category_theory_navbox&oldid=1672"

Navigation menu