## View abstract

### 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. document.getElementById('cloak24b15a7d76b058f7933725873168f4c5').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy24b15a7d76b058f7933725873168f4c5 = 'm&#97;t&#105;&#97;s.m&#101;nn&#105;' + '&#64;'; addy24b15a7d76b058f7933725873168f4c5 = addy24b15a7d76b058f7933725873168f4c5 + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_text24b15a7d76b058f7933725873168f4c5 = 'm&#97;t&#105;&#97;s.m&#101;nn&#105;' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloak24b15a7d76b058f7933725873168f4c5').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy24b15a7d76b058f7933725873168f4c5 + '\'>'+addy_text24b15a7d76b058f7933725873168f4c5+'<\/a>';

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.