4 papers
Directed homotopy theory, I. The fundamental category
Marco Grandis
Directed Algebraic Topology is beginning to emerge from various applications. The basic structure we shall use for such a theory, a 'd-space', is a topological space equipped with…
On the monad of proper factorisation systems in categories
Marco Grandis
It is known that factorisation systems in categories can be viewed as unitary pseudo algebras for the "squaring" monad in Cat. We show in this note that an analogous fact holds for…
An intrinsic homotopy theory for simplicial complexes, with applications to image analysis
Marco Grandis
A simplicial complex is a set equipped with a down-closed family of distinguished finite subsets. This structure, usually viewed as codifying a triangulated space, is used here dir…
Higher fundamental functors for simplicial sets
Marco Grandis
This is a sequel to a previous paper, developing an intrinsic, combinatorial homotopy theory for simplicial complexes; the latter form the cartesian closed subcategory of 'simple p…