In the mathematical discipline of category theory, a **strict initial object** is an initial object 0 of a category *C* with the property that every morphism in *C* with codomain 0 is an isomorphism. If *C* is a Cartesian closed category, then any initial object 0 of *C* is strict.^{[1]} Also, if *C* is a distributive or extensive category, then the initial object 0 of *C* is strict.^{[2]}

## References

**^**McLarty, Colin (4 June 1992).*Elementary Categories, Elementary Toposes*. Clarendon Press. ISBN 0191589497. Retrieved 13 February 2017.**^**Carboni, Aurelio; Lack, Stephen; Walters, R.F.C. (3 February 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.

## External links

This category theory-related article is a stub. You can help Wikipedia by expanding it. |