Geodesic
Continuous cohesion over sets
Theory and applications of categories, Tome 29 (2014), pp. 542-568 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

Voir la notice de l'article

A pre-cohesive geometric morphism $p:\cal E \rightarrow \cal S$ satisfies Continuity if the canonical $p_! (X^{p^* S}) \rightarrow (p_! X)^S$ is an iso for every $X$ in $\cal E$ and $S$ in $\cal S$. We show that if $\cal S = Set$ and $\cal E$ is a presheaf topos then, $p$ satisfies Continuity if and only if it is a quality type. Our proof of this characterization rests on a related result showing that Continuity and Sufficient Cohesion are incompatible for presheaf toposes. This incompatibility raises the question whether Continuity and Sufficient Cohesion are ever compatible for Grothendieck toposes. We show that the answer is positive by building some examples.

Publié le :
Classification : 18B25, 03G30
Keywords: topos, Axiomatic Cohesion 
@article{TAC_2014_29_a19,
     author = {Matias Menni},
     title = {Continuous cohesion over sets},
     journal = {Theory and applications of categories},
     pages = {542--568},
     year = {2014},
     volume = {29},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2014_29_a19/}
}
TY  - JOUR
AU  - Matias Menni
TI  - Continuous cohesion over sets
JO  - Theory and applications of categories
PY  - 2014
SP  - 542
EP  - 568
VL  - 29
UR  - http://geodesic.mathdoc.fr/item/TAC_2014_29_a19/
LA  - en
ID  - TAC_2014_29_a19
ER  - 
%0 Journal Article
%A Matias Menni
%T Continuous cohesion over sets
%J Theory and applications of categories
%D 2014
%P 542-568
%V 29
%U http://geodesic.mathdoc.fr/item/TAC_2014_29_a19/
%G en
%F TAC_2014_29_a19
Matias Menni. Continuous cohesion over sets. Theory and applications of categories, Tome 29 (2014), pp. 542-568. http://geodesic.mathdoc.fr/item/TAC_2014_29_a19/