Abstract
Fomin and Zelevinsky’s definition of cluster algebras laid the foundation for cluster theory. The various categorifications and generalizations of the original definition led to Iyama and Yoshino’s generalized cluster categories coming from positive-Calabi-Yau triples
Jin later defined simple minded collection quadruples
where the special case
is the analogue of Iyama and Yang’s triples: negative-Calabi-Yau triples. In this paper, we further study the quotient categories
coming from simple minded collection quadruples. Our main result uses limits and colimits to describe Hom-spaces over
in relation to the easier to understand Hom-spaces over
Moreover, we apply our theorem to give a different proof of a result by Jin: if we have a negative-Calabi-Yau triple, then
is a negative cluster category.