nLab bagdomain topos

Idea

The bagdomain topos construction is the topos analogue of the powerdomain construction in domain-theoretic database theory. Roughly speaking, an object $X$ is replaced by an object $X'$ such that points of $X'$ correspond to sets (=‘bags’) of points of $X$.

Related entries

• symmetric topos

• Artin gluing

• lax-idempotent 2-monad

References

• Marta Bunge, Jonathon Funk, Spreads and the Symmetric Topos , JPAA 113 (1996) pp.1-38.

• Marta Bunge, Jonathon Funk, Spreads and the Symmetric Topos II , JPAA 130 (1998) pp.49-84.

• Marta Bunge, Jonathon Funk, Singular Coverings of Toposes , Springer LNM 1890 Heidelberg 2006.

• M. Jibladze, Lower Bagdomain as a Glueing , Proc. A. Razmadze Math. Inst. 118 (1998) pp.33-41. (pdf)

• Peter Johnstone, Partial Products, Bagdomains and Hyperlocal Toposes , pp.315-339 in Fourman, Johnstone, Pitts (eds.), Applications of Categories in Computer Science - Proceedings of the LMS Symposium Durham 1991 , Cambridge UP 1992.

• Peter Johnstone, Variations on the Bagdomain Theme , Theo. Comp. Sci. 136 (1994) pp.3-20.

• Peter Johnstone, Sketches of an Elephant I , Oxford UP 2002. (sec. B4.4, pp.448-456)

• Steve Vickers, Geometric Theories and Databases , pp.288-314 in Fourman, Johnstone, Pitts (eds.), Applications of Categories in Computer Science - Proceedings of the LMS Symposium Durham 1991 , Cambridge UP 1992. (preprint)