I wanted to point this out and see if this is valid:

Since and , does that mean that ?

More generally, is it true that ?

I am inclined to think that this is the case, but maybe the way the multiplication is, i.e., , bars us from claiming so.

An example would be , where is as is in the problem statement. This clearly works, but does it work in general for functions ?

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### About El Niño

I'm a math geek. Math is fun!

I think so — the functions are in Hom which is a vector space.

Yes — they are evaluation maps:

Yes — they are evaluation maps: $latex \ + \ = \$

Wonderful! Well, based on the way the multiplication works on , the above result will very likely be of little consequence to the proof of the exercise, though it is still necessary.