A homomorphism from the affine Yangian $Y_{\mathrm{\hslash },\epsilon }(\widehat{\mathfrak{s}\mathfrak{l}}(n))$ to the affine Yangian $Y_{\mathrm{\hslash },\epsilon }(\widehat{\mathfrak{s}\mathfrak{l}}(n+1))$

We construct a homomorphism from the affine Yangian $Y_{\mathrm{\hslash },\epsilon }(\widehat{\mathfrak{s}\mathfrak{l}}(n))$ to the affine Yangian $Y_{\mathrm{\hslash },\epsilon }(\widehat{\mathfrak{s}\mathfrak{l}}(n+1))$. We also give the relationship between this homomorphism and the one from the affine Yangian $Y_{\mathrm{\hslash },\epsilon }(\widehat{\mathfrak{s}\mathfrak{l}}(n))$ to the universal enveloping algebra of the rectangular algebra ${\mathcal{W}}^k(\mathfrak{g}\mathfrak{l}(2n),(2^n))$ constructed by the author.