Definition:Object (Category Theory)
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Definition
Let $\mathbf C$ be a metacategory.
An object of $\mathbf C$ is an object which is considered to be atomic from a category theoretic perspective.
It is a conceptual device introduced mainly to make the discussion of morphisms more convenient.
Objects in a general metacategory are usually denoted with capital letters like $A,B,C,X,Y,Z$.
The collection of objects of $\mathbf C$ is denoted $\mathbf C_0$.
That objects don't play an important role in category theory is apparent from the fact that the notion of a metacategory can be described while avoiding to mention objects altogether.
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Nonetheless the notion of object is one of the two basic concepts of metacategories and as such of category theory.
Also see
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): object
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): object
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): object