Normalisation for the fundamental crossed complex of a simplicial set.
Normalizing the cyclic modules of Connes.
Note on homotopy pullbacks in abelian categories
On algebraic models for homotopy 3-types.
On derived categories and derived functors.
On flat covers in varieties
Flat covers do not exist in all varieties. We give a necessary condition for the existence of flat covers and some examples of varieties where not all algebras have flat covers.
On -disconnected injective models
Let be a finite group. It was observed by L.S. Scull that the original definition of the equivariant minimality in the -connected case is incorrect because of an error concerning algebraic properties. In the -disconnected case the orbit category was originally replaced by the category with one object for each component of each fixed point simplicial subsets of a -simplicial set , for all subgroups . We redefine the equivariant minimality and redevelop some results on the rational homotopy...
On the characterisation of Mal'tsev and Jónsson-Tarski algebras
There are very strong parallels between the properties of Mal'tsev and Jónsson-Tarski algebras, for example in the good behaviour of centrality and in the factorization of direct products. Moreover, the two classes between them include the majority of algebras that actually arise 'in nature'. As a contribution to the research programme building a unified theory capable of covering the two classes, along with other instances of good centrality and factorization, the paper presents a common framework...
On the geometry of intuitionistic S4 proofs.
On the homology theory of categories. I.
On the homology theory of categories. II.
On the nerve of an -category
On three types of simplicial objects
Opérations sur l'homologie cyclique des algèbres commutatives.
Parity complexes
Parity complexes : corrigenda
Question de Whitehead et modules précroisés
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...
Remarks about the Eilenberg-Zilber type decomposition in cosimplicial sets
Simplicial and categorical diagrams, and their equivariant applications.