Discrete Homotopy Theory

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About

Discrete homotopy theory is an emerging area of mathematics concerned with using homotopy-theoretic techniques to study combinatorial properties of (simple) graphs. It does so by introducing a new combinatorial notion of homotopy between graph maps and subsequently reinterpreting the usual homotopy-theoretic invariants, such as homotopy or homology groups, through the lenses of this new notion.

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Notes

• Graph
  • Some Examples of Graphs
• The Category of Garphs is Complete and Cocomplete
• The Category Graph is Monoidal
  • The Category Graph is Closed
• Paths in a graph
  • Path Component Functor on Graphs

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MOCs

• Graph Theory
• Category Theory
• Topology

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References