0P5F Proposition 4.1.1. The objects of the category 𝒰{\mathcal{U}} are the ene^{n}, n≥0n\geq 0. We have Hom(en,em)=0\operatorname{Hom}\nolimits(e^{n},e^{m})=0 if n≠mn\neq m and there is an isomorphism of differential algebras Hn→∼End(en),Ti↦ei−1τen−i−1.H_{n}\xrightarrow{\sim}\operatorname{End}\nolimits(e^{n}),\ T_{i}\mapsto e^{i-1}\tau e^{n-i-1}. There is a commutative diagram Hm⊗Hn\textstyle{H_{m}\otimes H_{n}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}Ti⊗Tj↦TiTm+j\scriptstyle{T_{i}\otimes T_{j}\mapsto T_{i}T_{m+j}}can\scriptstyle{{\mathrm{can}}}∼\scriptstyle{\sim}Hm+n\textstyle{H_{m+n}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}∼\scriptstyle{\sim}can\scriptstyle{{\mathrm{can}}}End(Em)⊗End(En)\textstyle{\operatorname{End}\nolimits(E^{m})\otimes\operatorname{End}\nolimits(E^{n})\ignorespaces\ignorespaces\ignorespaces\ignorespaces}⊗\scriptstyle{\otimes}End(Em+n)\textstyle{\operatorname{End}\nolimits(E^{m+n})}