/sci/ - Science & Math

Hi /mg/!

>>12251015
Yes. You would have [math](m_i) \in \ker( \bigoplus_i \varphi_i) \Leftrightarrow (\varphi_i(m_i)) = (0, 0, \dots) \Leftrightarrow m_i \in \ker( \varphi_i)[/math] for each [math]i[/math].

>>12252047
Given any surjection [math]f\colon A\to B[/math] and any morphism [math]g\colon \text{>>12251380}\to B[/math], there exists a morphism [math]h\colon \text{>>12251380} \to A[/math] such that [math]f\circ h = g[/math].