Relatively boolean and De Morgan toposes and locales
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 35 (1994) no. 3, pp. 249-261. 
@article{CTGDC_1994__35_3_249_0,
     author = {Kock, Anders and Reyes, Gonzalo E.},
     title = {Relatively boolean and {De} {Morgan} toposes and locales},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     pages = {249--261},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {35},
     number = {3},
     year = {1994},
     mrnumber = {1295120},
     zbl = {0806.18002},
     language = {en},
     url = {http://archive.numdam.org/item/CTGDC_1994__35_3_249_0/}
}
TY  - JOUR
AU  - Kock, Anders
AU  - Reyes, Gonzalo E.
TI  - Relatively boolean and De Morgan toposes and locales
JO  - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY  - 1994
SP  - 249
EP  - 261
VL  - 35
IS  - 3
PB  - Dunod éditeur, publié avec le concours du CNRS
UR  - http://archive.numdam.org/item/CTGDC_1994__35_3_249_0/
LA  - en
ID  - CTGDC_1994__35_3_249_0
ER  - 
%0 Journal Article
%A Kock, Anders
%A Reyes, Gonzalo E.
%T Relatively boolean and De Morgan toposes and locales
%J Cahiers de Topologie et Géométrie Différentielle Catégoriques
%D 1994
%P 249-261
%V 35
%N 3
%I Dunod éditeur, publié avec le concours du CNRS
%U http://archive.numdam.org/item/CTGDC_1994__35_3_249_0/
%G en
%F CTGDC_1994__35_3_249_0
Kock, Anders; Reyes, Gonzalo E. Relatively boolean and De Morgan toposes and locales. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 35 (1994) no. 3, pp. 249-261. http://archive.numdam.org/item/CTGDC_1994__35_3_249_0/

[1] M. Jibladze and P.T. Johnstone, The frame of fibrewise closed nuclei, Cahiers de Top. et Geom. Diff. Categorique 32 (1991), 99-112 | Numdam | MR | Zbl

[2] P.T. Johnstone, Conditions equivalent to de Morgan 's law, in Applications of Sheaves, Proceedings Durham 1977, Springer Lecture Notes in Math. 753 (1979), 479-491 | MR | Zbl

[3] P.T. Johnstone, Open maps of toposes, Manuscripta Math. 31 (1980), 214-247 | MR | Zbl

[4] P.T. Johnstone, Open locales and exponentiation, in Mathematical Applica tions of Category Theory, Contemporary Math. 30 (1984), 84-116 | MR | Zbl

[5] P.T. Johnstone, A constructive closed subgroup theorem, Cahiers de Top. et Geom. Diff. Categorique 30 (1989), 3-23 | Numdam | MR | Zbl

[6] A. Joyal and M. Tierney, An extension of the Galois Theory of Grothendieck, Mem. A.M.S. 309 (1984) | MR | Zbl

[7] A. Kock, Strong functors and monoidal monads, Arch. Math. 23 (1972), 113-120 | MR | Zbl

[8] A. Kock, Relatively Boolean toposes, Aarhus Preprint Series 1989/90 No. 21

[9] A. Kock, Algebras for the partial map classifier monad, in Category Theory, Proceedings Como 1990, Springer Lecture Notes in Math. 1488 (1991), 262-278 | MR | Zbl

[10] G.E. Reyes and H. Zolfaghari, Bi-Heyting algebras, toposes and modalities, to appear in Journal of Philosophical Logic | MR | Zbl

[11] R. Squire, Presheaf toposes and propositional logic, Ph.D. thesis, McMaster University 1990