- #1

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wouldnt this definition imply that id_A is a point instead of an arrow?

if not help me visualise this.

btw this should be the notation id_A:A->A

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- Thread starter MathematicalPhysicist
- Start date

In summary, for each object A in a category, there is an arrow id_A whose source and target are both A. This does not mean that id_A is a point, but rather a specific arrow from A to itself. In general, arrows cannot be identified with objects in a category. The terms "objects" and "arrows" are also preferred over "points" and "relations" in category theory. A helpful way to visualize this is to think of objects as boxes and morphisms as arrows, similar to a flow chart.

- #1

- 4,699

- 369

wouldnt this definition imply that id_A is a point instead of an arrow?

if not help me visualise this.

btw this should be the notation id_A:A->A

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- #2

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You may be thinking of the object as a single "point" and then identifying the arrow (from the object to itself) with that "point".

Remember that in general, given two objects in a category, there may be many arrows from one to another so you cannot identify arrows with objects. In particular, there may be many arrows from a given category to itself. The arrow "id_A" is a specific one of those so you certainly cannot identify "id_A" with the object.

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