#### Hall 123

#### Absence of Strøm-Hurewicz model structure on the category of graphs

#### Shuchita Goyal

##### IIT Bombay

*In this talk, we will first examine the notions of paths,*

products, double mapping cylinder object, etc in the category of graphs

similar to those in the category of topological spaces. We will show that

the double mapping cylinder in graphs defined analogous to the one in

spaces is not a correct candidate, and with respect to this notion of

double mapping cylinder, there cannot exist a Strøm-Hurewicz model

structure on the category of graphs.

Done