C. P. Kurtzman's evolving concepts of species, genus and higher categories

Evolving concepts regarding the genus Aeromonas: an expanding Panorama of species, disease presentations, and unanswered questions.

It has been almost 10 years since a major review on the association of Aeromonas with human disease has been published. During that period the number of valid species in the genus has grown to 14, with a new family (Aeromonadaceae) established to house this genus. Despite this explosion in the number of new genomospecies, only five (Aeromonas hydrophila, A. caviae, A. veronii, A. jandaei, and A...

On the Fukaya Categories of Higher Genus Surfaces

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.

Higher Operads, Higher Categories

AN INTRODUCTION TO HIGHER CLUSTER CATEGORIES

In this survey, we give an overview over some aspects of the set of tilting objects in an $m-$cluster category, with focus on those properties which are valid for all $m geq 1$. We focus on the following three combinatorial aspects: modeling the set of tilting objects using arcs in certain polygons, the generalized assicahedra of Fomin and Reading, and colored quiver mutation.

Directed Algebraic Topology, Categories and Higher Categories

Directed Algebraic Topology is a recent field, deeply linked with Category Theory. A ‘directed space’ has directed homotopies (generally non reversible), directed homology groups (enriched with a preorder) and fundamental n-categories (replacing the fundamental ngroupoids of the classical case). On the other hand, directed homotopy can give geometric models for lax higher categories. Applicatio...