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...

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [7] to adapt the machinery of globular operads [4] to this task. The resulting theory includes the Gray tensor product of 2-categories and the Crans tensor product [12] of Gray categories. Moreover much of the pre...

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...

We propose four axioms that a quasicategory should satisfy to be considered a reasonable homotopy theory of (∞, n)-categories. This axiomatization requires that a homotopy theory of (∞, n)-categories, when equipped with a small amount of extra structure, satisfies a simple, yet surprising, universal property. We further prove that the space of such quasicategories is homotopy equivalent to (RP∞...

It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n > 1. Recently the physical meaning of these higher categorical structures has been recognized and concrete examples of Extended TFTs have been constructed. Some of these examples, like the Rozansky-Witten model, are of geomet...

"C/"C ratios have been determined for plant tissue from 104 species representing 60 families. Higher plants fall into two categories, those with low 5PDB "3C values (-24 to -34%o) and those with high "3C values (-6 to -19%0). Algae have 8 "C values of -12 to -23%o. Photosynthetic fractionation leading to such values is discussed. Carbon isotope fractionation is associated with photosynthesis. T...

Abstract Let $\mathscr{C}$ be a $(d+2)$ -angulated category with d -suspension functor $\Sigma^d$ . Our main results show that every Serre on is functor. We also has $\mathbb{S}$ if and only Auslander–Reiten -angles. Moreover, $\tau_d=\mathbb{S}\Sigma^{-d}$ where $\tau_d$ -Auslander–Reiten translation. These generalize work by Bondal–Kapranov Reiten–Van den Bergh. As an application, we prove fo...