# Peter LeFanu Lumsdaine: Small-object arguments: algebraic, fat, enriched, oh my! (expository)

**Time: **
Wed 2019-03-20 10.00 - 11.45

**Location: **
Room 16, building 5, Kräftriket, Department of Mathematics, Stockholm University

**Lecturer: **
Peter LeFanu Lumsdaine, SU

Abstract: The *small object argument* is a versatile tool, originally introduced by Quillen for abstract homotopy theory, and since then adapted for a wide range applications in algebraic topology, logic, and pretty anywhere else that category theory is significantly used.

In this mainly expository talk, I’ll recall several versions of the small object argument, including at least

(a) the *algebraic* small object argument, introduced by Richard Garner (“Understanding the small object argument”, arxiv.org/abs/0712.0724 )

(b) the *fat* small object argument, introduced by Makkai, Rosický, and Vokřínek (“On a fat small object argument”, arxiv.org/abs/1304.6974 )

and look at their relationships and applications.