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Session S27 - Categories and Topology

Friday, July 16, 15:30 ~ 16:00 UTC-3

Spaces with decidable reflection

Matías Menni

Conicet and Universidad Nacional de La Plata, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In an extensive category with finite products we say that an object is $weakly\ locally\ connected\ (wlc)$ if it has a universal map towards a decidable object. We characterize wlc objects in ${\mathbf{Top}}$. We paraphrase a classical result by recalling that all affine schemes (over a base field) are wlc, and that the left adjoint ``$\pi_0$" to the subcategory of decidable objects preserves finite products. Also, we characterize the wlc objects in the (extensive) opposite of the category of MV-algebras. Moreover, if we let $\mathbf{MV}_{fp}$ be the category of finitely presentable MV-algebras then, as in the case of affine schemes, every object of $(\mathbf{MV}_{fp})^{op}$ is wlc and the associated left adjoint preserves finite products. By a well-known duality this may be seen as a statement about rational polyhedra and certain PL-maps between them.

Joint work with V. Marra.

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