In mathematics, an extensive category is a category C with finite coproducts that are disjoint and well-behaved with respect to pullbacks. Equivalently, C is extensive if the coproduct functor from the product of the slice categories C/X × C/Y to the slice category C/(X + Y) is an equivalence of categories for all objects X and Y of C.
Examples
The categories Set and Top of sets and topological spaces, respectively, are extensive categories. More generally, the category of presheaves on any small category is extensive.
The category CRing of affine schemes is extensive.
References
- Carboni, Aurelio; Lack, Stephen; Walters, R.F.C. (1993). "Introduction to extensive and distributive categories". Journal of Pure and Applied Algebra. 84 (2): 145–158. doi:10.1016/0022-4049(93)90035-R.
- ^ Pedicchio, Maria Cristina; Tholen, Walter (2004). Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory. Cambridge University Press. ISBN 978-0-521-83414-8. Retrieved 4 April 2018.
External links
- Extensive category at the nLab
 | This category theory-related article is a stub. You can help Misplaced Pages by expanding it. |