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I have a question about the construction of 2-morphisms from spans of spans in the paper "2-vector spaces and groupoid" by Jeffrey Morton .

Suppose we have a span of span of groupoids as follows and assume this diagram commutes. enter image description here

Now let $\epsilon_{L,t}$ is the counit for the left adjunction to $t$, and $\eta_{R,s}$ is the unit for the right adjunction associated to $s$. Then the author defines the natural transfromation $\Lambda(Y): (t_1)_*s_1^* \Rightarrow(t_2)_*s_2^*$ as $\Lambda(Y)=\epsilon_{L,t} \circ \eta_{R,s}$.

So this is the set up.

Now I think we have $\epsilon_{L,t}: Id_{[X_1, Vect]} \Rightarrow s_*s^*$ and $\eta_{R,s}: t_*t^* \Rightarrow Id_{[X_2, Vect]}$. The question is that how can we define the composite $\Lambda(Y)=\epsilon_{L,t} \circ \eta_{R,s}$ as above? Also why is it a natural transformation from $(t_1)_*s_1^*$ to $(t_2)_*s_2^*$?

I appreciate any help. Thank you in advance.

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