• Mathematics
  • Published 2001

Directed homotopy theory, I. The fundamental category

@inproceedings{Grandis2001DirectedHT,
  title={Directed homotopy theory, I. The fundamental category},
  author={Marco Grandis},
  year={2001}
}
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 a family of 'directed paths', closed under some operations. This allows for 'directed homotopies', generally non reversible, represented by a cylinder and cocylinder functors. The existence of 'pastings' (colimits) yields a geometric realisation of cubical sets as d-spaces, together with homotopy constructs which… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 31 CITATIONS

Stratified spaces, Directed Algebraic Topology, and State-Sum TQFTs

VIEW 7 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Streams, d-Spaces and Their Fundamental Categories

VIEW 8 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Towards Modelling of Hybrid Systems

  • Rafal Wisniewski
  • Computer Science
  • Proceedings of the 45th IEEE Conference on Decision and Control
  • 2006
VIEW 7 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

CATEGORIES OF COMPONENTS AND LOOP-FREE CATEGORIES

VIEW 4 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Components of the Fundamental Category

VIEW 4 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Stable Components of Directed Spaces