Extensive category

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.

gollark: Or so.
gollark: You can get the pi zero for £/$5.
gollark: With those fancy LED modules they have for them you could have amazing high-res blinky light arrays.
gollark: So just get a few RPis.
gollark: Make them flicker on and off uselessly.

References
  1. 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. 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.


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