I'm stuck on a very simple question: Let $\Delta^1$ be the simplicial set, so $(\Delta^1)_n = Hom([n], [1])$ is the set of nondecreasing functions $f:\{0, 1, \ldots, n\} \to \{0,1 \}$. Let $sSets$ be the category of simplicial sets.
What exactly are the elements of the set $Hom_{sSets}(\Delta^1 \times \Delta^1, \Delta^1)$ ?
I know the $n$ simplices of $(\Delta^1 \times \Delta^1)_n = (\Delta^1)_n \times (\Delta^1)_n$ and I'm guessing I only need to worry about $n=1$ because the face and dengenracy maps will then determine values for higher $n$. $(\Delta^1)_1=Hom([1], [1])$ has three elements, namely $00$, $01$, $11$ - the notation is these are the images of a map $[1] \to [1]$.