Colimits for the pro-category of towers of simplicial sets
Combinatorial homology in a perspective of image analysis.
Combinatorial Laplacian of the matching complex.
Combinatoric of syzygies for semigroup algebras.
We describe how the graded minimal resolution of certain semigroup algebras is related to the combinatorics of some simplicial complexes. We obtain characterizations of the Cohen-Macaulay and Gorenstein conditions. The Cohen-Macaulay type is computed from combinatorics. As an application, we compute explicitly the graded minimal resolution of monomial both affine and simplicial projective surfaces.
Combinatorics of branchings in higher dimensional automata.
Computation of cohomology operations on finite simplicial complexes.
Conditions For A Realization Functor To Commute With Finite Products.
Construction géométrique des idempotents eulériens. Filtration des groupes de polytopes et des groupes d'homologie de Hochschild
Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group
We prove that Alexander-Spanier cohomology with coefficients in a topologicalAbelian group G is isomorphic to the group of isomorphism classes of principal bundles with certain Abelian structure groups. The result holds if either X is a CW-space and G arbitrary or if X is metrizable or compact Hausdorff and G an ANR.
Contractible simplicial objects
We raise the question of when a simplicial object in a catetgory is deemed contractible. The literature offers three definitions. One is the existence of an “extra degeneracy”, indexed by , which does not quite live up to the name. This can be strengthened to a “strong extra degeneracy". Another possibility is that it be homotopic to a constant simplicial object. Despite claims in the literature to the contrary, we show that all three are distinct concepts with strong extra degeneracy implies extra...
Coxeter-like complexes.
Cubical sets and their site.
Cyclic homology, a survey
Diagonal fibrations are pointwise fibrations.
Equilogical spaces, homology and non-commutative geometry
Finite sets and symmetric simplicial sets.
Finite simplicial multicomplexes.
Free crossed resolutions from simplicial resolutions with given -basis
Free minimal resolutions and the Betti numbers of the suspension of an -gon.
From cubical to globular higher categories