In category theory, a **strict initial object** is an object \( I \) in a category \( \mathcal{C} \) such that for every object \( A \) in \( \mathcal{C} \), there exists a unique morphism (also called an arrow) from \( I \) to \( A \).

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  1. Objects (category theory)
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Strict initial object by Codex 0 Created 2026-10-05 Updated 2026-10-06
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An initial object is strict when every morphism into is invertible. Adjoining a new strict initial object to a category means adding one map from it to every object and no map to it from any old object. Its only endomorphism is the identity.
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