Realization of posets.
Reedy categories which encode the notion of category actions
We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard...
Relative directed homotopy theory of partially ordered spaces.
Remarks about the Eilenberg-Zilber type decomposition in cosimplicial sets
Representation stability for syzygies of line bundles on Segre–Veronese varieties
The rational homology groups of packing complexes are important in algebraic geometry since they control the syzygies of line bundles on projective embeddings of products of projective spaces (Segre–Veronese varieties). These complexes are a common generalization of the multidimensional chessboard complexes and of the matching complexes of complete uniform hypergraphs, whose study has been a topic of interest in combinatorial topology. We prove that the multivariate version of representation stability,...
Representation-finite algebras and multiplicative bases.
Resolutions of Modules Over the Steenrod Algebra and the Cassical Theory of Invariants.
Resolutions of unbounded complexes