Fix a category. For any two objects, A and B, therein, write A ≈B if there exists an isomorphism

Question

Fix a category. For any two objects, $A$ and $B$, therein, write $A \approx B$ if there exists an isomorphism from $A$ to $B$. Prove that " $\approx$ " is an equivalence relation. What are the equivalence classes?

   Fix a category. For any two objects, $A$ and $B$, therein, write $A \approx B$ if there exists an isomorphism from $A$ to $B$. Prove that " $\approx$ " is an equivalence relation. What are the equivalence classes?

Mathematical physics

Robert Geroch 1st Edition

Chapter 8, Problem 60

Thanks for your feedback!

Fix a category. For any two objects, $A$ and $B$, therein, write $A \approx B$ if there exists an isomorphism from $A$ to $B$. Prove that " $\approx$ " is an equivalence relation. What are the equivalence classes?

Play audio

Feedback

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later

Please give Ace some feedback