Strict initial object

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
  1. McLarty, Colin (4 June 1992). Elementary Categories, Elementary Toposes. Clarendon Press. ISBN 0191589497. Retrieved 13 February 2017.
  2. 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.
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