Definition of "surjection"

In some special cases, however, the number of surjections A → B {\displaystyle A\rightarrow B} can be identified.

1992, Rowan Garnier, John Taylor, Discrete Mathematics for New Technology, Institute of Physics Publishing, page 220

Let J = ∩ i m i {\displaystyle J=\cap _{i}m_{i}} be the (irredundant) primary decomposition of J {\displaystyle J} . We associate to the pair ( J , ω ) {\displaystyle (J,\omega )} the element ∑ i ( m i , ω i ) ∈ G {\displaystyle \textstyle \sum _{i}(m_{i},\omega _{i})\in G} , where ω i {\displaystyle \omega _{i}} is the equivalence class of surjections from L / m i L ⊕ ( A / m i ) n − 1 {\displaystyle L/m_{i}L\oplus (A/m_{i})^{n-1}} to m i / m i 2 {\displaystyle m_{i}/m_{i}^{2}} induced by ω {\displaystyle \omega } .

1999, M. Pavaman Murthy, “A survey of obstruction theory for projective modules of top rank”, in Tsit-Yuen Lam, Andy R. Magid, editors, Algebra, K-theory, Groups, and Education: On the Occasion of Hyman Bass's 65th Birthday, American Mathematical Society, page 168

In Banach space theory, a mapping u : E → F {\displaystyle u:E\rightarrow F} (between Banach spaces) is called a metric surjection if it is onto and if the associated mapping from E / ker ( u ) {\displaystyle E/{\text{ker}}(u)} to F {\displaystyle F} is an isometric isomorphism. Moreover, by the classical open mapping theorem, u {\displaystyle u} is a surjection iff the associated mapping from E / ker ( u ) {\displaystyle E/{\text{ker}}(u)} to F {\displaystyle F} is an isomorphism.

2003, Gilles Pisier, Introduction to Operator Space Theory, Cambridge University Press, page 43