Extensive category
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Short description: Type of category in mathematics
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.[1]
Examples
The categories Set and Top of sets and topological spaces, respectively, are extensive categories.[2] More generally, the category of presheaves on any small category is extensive.[2]
The category CRingop 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.
- ↑ 2.0 2.1 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. https://books.google.com/books?id=WHudOFwuMn8C&pg=PA342. Retrieved 4 April 2018.
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