Year: 2026
Type: preprint
Abstract: We introduce reparametrization categories with cuts. For every such category $\mathcal{P}$, the tensor product of two objectwise weak homotopy equivalences of $\mathcal{P}$-spaces is an objectwise weak homotopy equivalence, and the q-model structure on $\mathcal{P}$-flows is left proper. The reparametrization categories $\mathcal{G}$ and $\mathcal{M}$, as well as the terminal category $\mathbf{1}$, have cuts. The terminal category recovers the left properness of the q-model structure on ordinary flows. We also give a symmetric reparametrization category with cuts and a strict unit. This category is not equivalent to $\mathbf{1}$.
Source: arXiv (Cornell University)
Author: Gaucher, Philippe
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203489210
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