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math.AT2001
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…
math.AT2000
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…
math.AT2000
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…