If "Z" is a Cartier divisor, then under mild hypotheses on φ, there is a pullback φ*"Z". Sheaf-theoretically, when there is a pullback map , then this pullback can be used to define pullback of Cartier divisors. In terms of local sections, the pullback of formula_68 is defined to be formula_77. Pullback is always defined if φ is dominant, but it cannot be defined in general. For example, if and φ is the inclusion of "Z" into "Y", then φ*"Z" is undefined because the corresponding local sections would be everywhere zero. (The pullback of the corresponding line bundle, however, is defined.)