A negative Calabi-Yau version of discrete cluster categories

Igusa-Todorov discrete cluster categories are an infinite discrete generalisation of the classical cluster category of type A. These are triangulated categories having 2 Calabi-Yau dimension, i.e. their Ext spaces are symmetric.

Our aim is to introduce a (-1)-Calabi-Yau version of Igusa-Todorov discrete cluster categories. To do so, we define the category of infinite discrete symmetric Nakayama representations by using the notion of continuous Nakayama representations introduced by Rock and Zhu.