Science Talk

barsony · Guest

Hi,
I had two questions concerning terminal objects. I hope anyone can help me.

1. How to prove formally that A is isomorphic to A x T, the categorical
product of A and a terminal object T? For example A ~ Ax1.

From the universal property of products it follows there is a unique arrow u
: A ---> A x 1 such that p_A u = id_A. (p_A is the projection A x 1 ---> A).
But why is u p_A = id_A as well?

2. If id_A is constant (i.e. it factors through a terminal object T) how
does it follow that A ~ T?

thanks for any help
-- barsony --