We extend all known results about transferred model structures on algebraically cofibrant
and fibrant objects by working with weak model categories. We show that for an accessible …

Using Reedy techniques, this paper gives a correct proof of the left properness of the q-
model structure of flows. It fixes the preceding proof which relies on an incorrect argument …

We investigate the extent to which the weak equivalences in a model category can be
equipped with algebraic structure. We prove, for instance, that there exists a monad T such …

We present a slight variation on a notion of weak∞-groupoid introduced by Grothendieck in
Pursuing Stacks and we study the homotopy theory of these∞-groupoids. We prove that the …

We introduce and study a notion of cylinder coherator similar to the notion of Grothendieck
coherator which define more flexible notion of weak infinity groupoids. We show that each …

Algebraic injectivity was introduced to capture homotopical structures like algebraic Kan
complexes. But at a much simpler level, it allows one to describe sets with operations …

We introduce a notion of signature whose sorts form a direct category, and study computads
for such signatures. Algebras for such a signature are presheaves with an interpretation of …

In this article, we introduce the notion of a curved absolute L∞-algebra, a structure that
behaves like a curved L∞-algebra where all infinite sums of operations are well-defined by …

Spaces as infinity-groupoids Page 267 5 Spaces as Infinity-Groupoids Timothy Porter Contents
258 260 273 1 Introduction 2 The Beginnings: Recollections of Poincare’s Fundamental …

The goal of this paper is to address the problem of building a path object for the category of
Grothendieck (weak)∞-groupoids. This is the missing piece for a proof of Grothendieck's …