Template:Category theory navbox

From Maths

Revision as of 21:00, 3 February 2016 by Alec (Talk | contribs) (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;...")

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

Jump to: navigation, search

[Expand] v • d • e Category Theory

Overview of the concepts of Category Theory

Key objects	Category, Functor (Covariant, Contravariant), Subcategory	$\xymatrix{ & \text{Arrow} \\ \text{Monic} \ar@{^{(}->}[ur] & & \text{Epic} \ar@{^{(}->}[ul] \\ & \text{Bimorphism} \ar@{^{(}->}[ur] \ar@<-0.5ex>@{^{(}->}[ul] \\ \text{Split monic} \ar@{^{(}->}[uu] & & \text{Split epic} \ar@<-0.75ex>@{^{(}->}[uu] \\ & \text{Isomorphism} \ar@{^{(}->}[ur] \ar@<-0.5ex>@{^{(}->}[ul] \ar@{^{(}->}[uu] }$

Typical morphism types (see diagram on right)	Arrow (AKA: Morphism), Monic, Epic, Bimorphism, Split monic (AKA: Section), Split epic (AKA: Retraction), Isomorphism

Key objects	$\text{Initial}$ , $\text{Final}$

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	SET, Pfn, GROUP

TODO: fill this out

TODO: Can diagram be any neater?

Retrieved from "https://wiki.unifiedmathematics.com/index.php?title=Template:Category_theory_navbox&oldid=1583"

Categories:

Template:Category theory navbox

Navigation menu

Views

Personal tools

Navigation

Search

Tools