Elementary Category Theory  3

 Community Team
 Posts: 314
 Joined: Tue Nov 10, 2015 8:25 pm
Elementary Category Theory  3
Let \( \mathcal{C} \) be an abelian category and let \( f \ \colon X \longrightarrow Y \) be a morphism in \( \mathcal{C} \). Show that the diagram
\[ \xymatrix{ K \ar[d] \ar[r]^{0_{K}} & 0 \ar[d] \\ X \ar[r]_f &Y} \]
is a pullback diagram if and only if \( K = Ker(f) \).
\[ \xymatrix{ K \ar[d] \ar[r]^{0_{K}} & 0 \ar[d] \\ X \ar[r]_f &Y} \]
is a pullback diagram if and only if \( K = Ker(f) \).
Create an account or sign in to join the discussion
You need to be a member in order to post a reply
Create an account
Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute
Sign in
Who is online
Users browsing this forum: No registered users and 1 guest