Lambda-presentable morphisms, injectivity and (weak) factorization systems

Details Lambda-presentable morphisms, injectivity and (weak) factorization systems Lambda-presentable morphisms, injectivity and (weak) factorization systems

2005-09-14

arxiv.org/abs/math/0509318v1

Applied Categorical Structures 14 (2006) 273-286 (http://springerlink.metapress.com/content/1572-9095/)

Mathematics

Category Theory

16 pages

Scientific paper

We show that in a locally lambda-presentable category, every lambda(m)-injectivity class (i.e., the class of all the objects injective with respect to some class of lambda-presentable morphisms) is a weakly reflective subcategory determined by a functorial weak factorization system cofibrantly generated by a class of lambda-presentable morphisms. This was known for small-injectivity classes, and referred to as the "small object argument". An analogous result is obtained for orthogonality classes and factorization systems, where lambda-filtered colimits play the role of the transfinite compositions in the injectivity case. Lambda-presentable morphisms are also used to organize and clarify some related results (and their proofs), in particular on the existence of enough injectives (resp. pure-injectives).

Affiliated with

Also associated with

No associations

Rating

Lambda-presentable morphisms, injectivity and (weak) factorization systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lambda-presentable morphisms, injectivity and (weak) factorization systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lambda-presentable morphisms, injectivity and (weak) factorization systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-680532