PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: Very high Entry average rating: No information on entry rating
discrete category (Definition)

A category $ \mathcal{C}$ is said to be a discrete category if the only morphisms in $ \mathcal{C}$ are the identity morphisms associated with each of the objects in $ \mathcal{C}$.

A discrete category with one object is called a trivial category. A discrete category with no objects is called the empty category.

Remark. Given any category $ \mathcal{C}$, the smallest subcategory consisting of all objects in $ \mathcal{C}$ is discrete, which is also the largest discrete subcategory in $ \mathcal{C}$ (largest in the sense that it contains all objects of $ \mathcal{C}$). For every object $ X\in \mathcal{C}$, we can associate the trivial category $ \mathcal{C}_X$ consisting of one object, $ X$, and one morphism $ 1_X$.



"discrete category" is owned by CWoo.
(view preamble)

View style:

Also defines:  trivial category, empty category
Log in to rate this entry.
(view current ratings)

Cross-references: associate, contains, discrete, subcategory, objects, identity, morphisms, category
There are 5 references to this entry.

This is version 2 of discrete category, born on 2006-09-16, modified 2007-10-24.
Object id is 8357, canonical name is DiscreteCategory.
Accessed 865 times total.

Classification:
AMS MSC18A05 (Category theory; homological algebra :: General theory of categories and functors :: Definitions, generalizations)

Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)