We study higher cluster tilting objects in generalized higher cluster categories arising from dg algebras of higher Calabi-Yau dimension. Taking advantage of silting mutations of Aihara-Iyama, we obtain a class of m-cluster tilting objects in generalized m-cluster categories. For generalized m-cluster categories arising from strongly (m + 2)-Calabi-Yau dg algebras, by using truncations of minim...

We prove the existence of an m-cluster tilting object in a generalized m-cluster category which is (m+1)-Calabi–Yau andHom-finite, arising froman (m+2)-Calabi–Yau dg algebra. This is a generalization of the result for them = 1 case in Amiot’s Ph.D. thesis. Our results apply in particular to higher cluster categories associated to Ginzburg dg categories coming from suitable graded quivers with s...

We present a new way in which to model biological processes using graphical inputs and outputs. This method is grounded in higher category theory and can be viewed as an extension of the popular Petri net approach for biological modelling. We implement a stochastic process algorithm in globular, a rewriting program for higher categories. We use this to model a basic viral invasion process, foll...

We construct the Fukaya category of a closed surface equipped with an area form using only elementary (essentially combinatorial) methods. We also compute the Grothendieck group of its derived category.

This paper lists for the first time many of the names that have been used for fungal groups above the rank of order. Full bibliographic references are provided for the location where the name was first introduced together with comments on ranks, orthography, typification and the provision of descriptions or diagnoses. More general remarks are made about the nomenclature of higher taxa and the n...