ScalingStacks

Remark 3.3. The fact that one describes factorization homology as either a coend or a left Kan extension is exactly analogous to a more familiar fact about the geometric realizations of a simplicial set $X_{\bullet}$: one can think of geometric realization as a coend (this is the usual definition, given as a quotient of $\coprod_{i}X_{i}\times\Delta^{i}$), or one can think of it as a left Kan extension (the colimit of the overcategory of simplices in $X_{\bullet}$ of the functor which sends the simplicial $i$-simplex $\Delta[i]$ to the topological $i$-simplex $\Delta^{i}$).