The uniform homotopy category

Homotopy Coherent Category Theory

The Homotopy Type of the Cobordism Category

Homotopy Representations over the Orbit Category

Let G be a finite group. The unit sphere in a finitedimensional orthogonal G-representation motivates the definition of homotopy representations, due to tom Dieck. We introduce an algebraic analogue and establish its basic properties, including the Borel–Smith conditions and realization by finite G-CW-complexes.

A Convenient Category for Directed Homotopy

We propose a convenient category for directed homotopy consisting of preordered topological spaces generated by cubes. Its main advantage is that, like the category of topological spaces generated by simplices suggested by J. H. Smith, it is locally presentable.

Khovanov Homotopy Type, Burnside Category, and Products

In this paper, we give a new construction of a Khovanov homotopy type. We show that this construction gives a space stably homotopy equivalent to the Khovanov homotopy types constructed in [LS14a] and [HKK] and, as a corollary, that those two constructions give equivalent spaces. We show that the construction behaves well with respect to disjoint unions, connected sums and mirrors, verifying se...