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arXiv · 2608.03837

Compact-Open Dualities for Stably Continuous Posets

Jérémie Marquès
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Abstract

We organize and generalize several dualities involving continuous posets. The main theorem reads $\mathbf{St}_\alpha\mathbf{Inf}_{\alpha'}\mathbf{Cont}_{\beta'}\mathbf{Sup}_\beta \simeq (\mathbf{St}_\beta\mathbf{Inf}_{\beta'}\mathbf{Cont}_{\alpha'}\mathbf{Sup}_\alpha)^{\mathrm{op}}$, where $\mathbf{St}$, $\mathbf{Inf}$, $\mathbf{Cont}$ and $\mathbf{Sup}$ refer to stability, completeness, continuity and cocompleteness. The indices are "ladders", i.e., classes of sets $\lambda$ stable under dependent sums and quotients, with associated notions of $\lambda$-small infima and ${\lambda}$-filtered suprema. In the second half of the paper, we discuss algebraicity, proximity lattices and perfect maps.

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Jérémie Marquès. 2026-08-04. Compact-Open Dualities for Stably Continuous Posets. https://arxiv.org/abs/2608.03837

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