Maths - Category Theory - Weak Equivilance

Weak equivilance provides a simpler way to determine equivilance.

On the equivilance page we discussed how to determine equivilance by finding two functors. F and G, which give the identity when composed in both directions. equivilance
equivilance
Weak equivilance gives us a way to do this using only a functor in one direction F. However this only tells us that an equivilance exists, not the functors which give the equivilance. weak equivilance

Given this functor F : C → D there is an equivalence if and only if the following are all true:

Further Information

Weak equivalence was first used in algebraic topology, in particular, in model category theory as described on the page here.


metadata block
see also:

Adjunctions from Morphisms

Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

 

Terminology and Notation

Specific to this page here:

 

This site may have errors. Don't use for critical systems.

Copyright (c) 1998-2021 Martin John Baker - All rights reserved - privacy policy.