Definition talk:Composition of Mappings

Ok, so who hid the Composite Mapping is Mapping page? --Lord_Farin 20:37, 7 August 2012 (UTC)


 * Was never any such page. This is one of the earliest pages on PW, from before it was all rigorous and all that. --prime mover 20:46, 7 August 2012 (UTC)


 * Don't we only need the domain of $f_2$ to include the image of $f_1$, rather than equaling its codomain? --Dfeuer (talk) 19:28, 5 March 2013 (UTC)


 * It doesn't really matter (the codomain can be enlarged if necessary). However, categorical perspective makes the current the most desirable definition. &mdash; Lord_Farin (talk) 19:40, 5 March 2013 (UTC)


 * And I just realized associativity could be an issue too. I guess Composition of Relations will cover any actual need for this generalization. --Dfeuer (talk) 19:43, 5 March 2013 (UTC)


 * Problem with Composition of Mappings is Associative? Where? Without working through it headachingly, I can't see it. --prime mover (talk) 21:55, 6 March 2013 (UTC)

It could be that $\operatorname{im}(f_2 \circ f_1) \subseteq \operatorname{dom} f_3$ while $f_3 \circ f_2$ is not defined on all of $\operatorname{dom} f_2$ if we allow for the above convention. &mdash; Lord_Farin (talk) 22:03, 6 March 2013 (UTC)


 * PM: nothing to see here. I had a bad idea. Move along. --Dfeuer (talk) 22:30, 6 March 2013 (UTC)

Refactor
The binary operation bit could be factored out into "composition operation/mappings" or some such, no? --Dfeuer (talk) 21:18, 16 April 2013 (UTC)