# Inessential directed maps and directed homotopy equivalences

@article{Raussen2021InessentialDM, title={Inessential directed maps and directed homotopy equivalences}, author={Martin Raussen}, journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, year={2021}, volume={151}, pages={1383 - 1406} }

A directed space is a topological space $X$ together with a subspace $\vec {P}(X)\subset X^I$ of directed paths on $X$. A symmetry of a directed space should therefore respect both the topology of the underlying space and the topology of the associated spaces $\vec {P}(X)_-^+$ of directed paths between a source ($-$) and a target ($+$)—up to homotopy. If it is, moreover, homotopic to the identity map—in a directed sense—such a symmetry will be called an inessential d-map, and the paper explores…

## One Citation

### Pair component categories for directed spaces

- MathematicsJ. Appl. Comput. Topol.
- 2020

A pair component category as quotient category is constructed: it has as objects pair components along which the homotopy type is invariant—for a coherent and transparent reason and gives reasonable results for spaces with non-trivial directed loops.

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