T such that tu factors through fg . Then tu also factors through f . This shows that f is unipotent. Suppose S and T are two sets of maps to Y . The pullbacks of normal monos are normal monos.
Y are two normal monos.
This shows that fg is normal. If A is an analytic category then any singular or analytic mono is normal. If A has pullbacks, then a mono is normal iff its pullback along any map is not proper unipotent. X is a mono. Conversely, assume the condition is satisfied.