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Can someone explain how to reconcile the approach of Awodey with the approach of Aluffi/Leinster ... presumably the two approaches are actually the same ...

The books I am referring to are as follows:

Algebra: Chapter 0 by Paolo Aluffi

Category Theory by Steve Awodey

Basic Category Theory by Tom LeinsterThe approaches to the construction of a product category are as follows:

**Awodey**

https://www.physicsforums.com/attachments/8361

https://www.physicsforums.com/attachments/8362

**Aluffi**

View attachment 8363

**Leinster**

View attachment 8364

View attachment 8365

As I mentioned above ... my question is as follows:

How do we reconcile the approach of Awodey to the construction of a product category with the approach of Aluffi/Leinster ... ?

Hope someone can help ...

Peter