Physics Library
 An open source physics library
Encyclopedia | Forums | Docs | Random | Template Test |  
Login
create new user
Username:
Password:
forget your password?
Main Menu
Sections

Talkback

Downloads

Information
fully faithful functor (Definition)
Definition 0.1   Let $\mathcal{A}$ and $\mathcal{B}$ be two categories and let $F: \mathcal{A} \to \mathcal{B}$ be a functor. $F$ is said to be a fully faithful functor if it is an isomorphism on every set $Hom(-,-)$ of morphisms, and that it is essentially surjective if for every object $X \in \mathcal{B}$, there is some $Y \in \mathcal{A}$ such that $X$ and $F(Y)$ are isomorphic.



"fully faithful functor" is owned by bci1.

View style:

See Also: Yoneda lemma

Keywords:  functor, fully faithful, equivalence of categories

Cross-references: object, surjective, morphisms, isomorphism, functor, categories
There are 2 references to this object.

This is version 4 of fully faithful functor, born on 2009-06-15, modified 2009-06-15.
Object id is 799, canonical name is FullyFaithfulFunctor2.
Accessed 497 times total.

Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:

No messages.

Testing some escape charachters for html category with a generator has an injective cogenerator" now escape ” with "