Hey


Is there a universal property for the smash product (of pointed spaces or pointed CW-complexes or something of that ilk)? I've seen the smash product of spectra defined with a universal property in terms of the smash product of pointed-spaces, but I was wondering if there was just some simple universal property you could put on these somewhat mysterious (to me) space-level operations.


EDIT: I was hoping for something more satisfying than the internal Hom adjoint. The tensor product can be defined similarly, but I find the universal product in terms of bilinear maps more intuitive (although, when unraveled, they are the same thing). I was hoping for something similar for smash. 


Thanks :)



Universal Property of the Smash Product (of pointed spaces)
$X \wedge Y$ represents maps from $X \times Y$ that are base-point-preserving separately in each variable, just as the tensor product represents maps that are linear separately in each variable.


