Initial Object

up:: 027 MOC Category Theory

Given a Category , we say an object is an initial object if all objects have a morphism from to . That is,

Properties

• An initial object is a Terminal Object in the Opposite Category .
• A terminal object is isomorphic to an initial object if there is a morphism from T to I.
• An initial object which is also terminal is called a Zero Object.

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References

• KASHIWARA, Masaki; SCHAPIRA, Pierre, Categories and Sheaves, Berlin, Heidelberg: Springer Berlin Heidelberg, 2006.
• Summary of Truth about Types, a talk by Bartosz Milewski - Rakhim.org