# Set notation for generalized elements

I am currently reading Steve Awodey's book on category theory. On pg. 101 he uses set notation for generalized elements, namely $\{ a \mid f(a) = g(a) \}$ What does it mean in an arbitrary category?

• It means the pullback of $f$ and $g$. – Qiaochu Yuan Mar 19 '15 at 6:07
• The pullback would be $\{ (a, b) : f (a) = g ( b) \}$. This is the equaliser. – Zhen Lin Mar 19 '15 at 6:44
• So that's basically a syntax for some limits. Thanks. – Konstantin Solomatov Mar 19 '15 at 17:44