Geodesic
Bi-directional models of `Radically Synthetic' Differential Geometry
Theory and applications of categories, Bunge Festschrift, Tome 40 (2024), pp. 413-429

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

The radically synthetic foundation for smooth geometry formulated in [Law11] postulates a space T with the property that it has a unique point and, out of the monoid T^T of endomorphisms, it extracts a submonoid R which, in many cases, is the (commutative) multiplication of a rig structure. The rig R is said to be bi-directional if its subobject of invertible elements has two connected components. In this case, R may be equipped with a pre-order compatible with the rig structure. We adjust the construction of `well-adapted' models of Synthetic Differential Geometry in order to build the first pre-cohesive toposes with a bi-directional R. We also show that, in one of these pre-cohesive variants, the pre-order on R, derived radically synthetically from bi-directionality, coincides with that defined in the original model.

Publié le :
Classification : 58A03, 18B25, 18F10, 03G30
Keywords: Axiomatic Cohesion, (Radically) Synthetic Differential Geometry 
@article{TAC_2024_40_a14,
     author = {Mat{\'\i}as Menni},
     title = {Bi-directional models of {`Radically} {Synthetic'} {Differential} {Geometry}},
     journal = {Theory and applications of categories},
     pages = {413--429},
     publisher = {mathdoc},
     volume = {40},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_40_a14/}
}
TY  - JOUR
AU  - Matías Menni
TI  - Bi-directional models of `Radically Synthetic' Differential Geometry
JO  - Theory and applications of categories
PY  - 2024
SP  - 413
EP  - 429
VL  - 40
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2024_40_a14/
LA  - en
ID  - TAC_2024_40_a14
ER  - 
%0 Journal Article
%A Matías Menni
%T Bi-directional models of `Radically Synthetic' Differential Geometry
%J Theory and applications of categories
%D 2024
%P 413-429
%V 40
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2024_40_a14/
%G en
%F TAC_2024_40_a14
Matías Menni. Bi-directional models of `Radically Synthetic' Differential Geometry. Theory and applications of categories, Bunge Festschrift, Tome 40 (2024), pp. 413-429. http://geodesic.mathdoc.fr/item/TAC_2024_40_a14/