The purpose of this short paper is to analyse limits and colimits in the category Part of partial groups, algebraic structures introduced by A. Chermak. The class of partial groups contains a subclass of objects corresponding to the class of transporter systems as defined by Oliver and Ventura. Special cases of such transporter systems are the centric linking systems associated to saturated fusion systems that were defined by Broto, Levi and Oliver. We will prove that Part is both complete and… Expand

It is well known that not every finite group arises as the full automorphism group of some group. Here we show that the situation is dramatically different when considering the category of partial… Expand

The main goal of this paper is to identify and study a certain class of spaces which in many ways behave like p-completed classifying spaces of finite groups. These spaces occur as the “classifying… Expand

A partial group is a generalization of the concept of group recently introduced by A. Chermak. By considering partial groups as simplicial sets, we propose an extension theory for partial groups… Expand

homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition,… Expand

We study extensions of p-local finite groups where the kernel is a p-group. In particular, we construct examples of saturated fusion systems $${\mathcal{F}}$$ which do not come from finite groups,… Expand

We introduce objective partial groups, of which the linking systems and p-local finite groups of Broto, Levi, and Oliver, the transporter systems of Oliver and Ventura, and the… Expand