Functions that can be written as direct products of other functions; question about terminology and notation - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T08:12:40Z http://mathoverflow.net/feeds/question/106496 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/106496/functions-that-can-be-written-as-direct-products-of-other-functions-question-abo Functions that can be written as direct products of other functions; question about terminology and notation user1837 2012-09-06T11:00:25Z 2012-09-06T11:24:10Z <p>Let $$f : X_0 \rightarrow Y_0, \;\;\; g:X_1 \rightarrow Y_1$$ and define that the "direct product" of $f$ and $g$ is a map $$f \otimes g : (X_0 \times X_1) \rightarrow (Y_0 \times Y_1), \mbox{ such that } (f \otimes g)(x_0,x_1)=(f(x_0),g(x_1)).$$</p> <p>Question 1. What is the standard terminology/notation for this concept?</p> <p>Now given a function $h$, it's possible that $h$ has the property that there exist $f$ and $g$ such that $$h = f \otimes g$$ Question 2. What is the name of this property?</p>