# 2021-10-13

## 00:18

• A bit on lambda sequences :
• Let $$\Lambda$$ be the category of based finite sets $$\mathbf{n}=\{0,1,2, \cdots, n\}$$ with base point 0 and based injections. The morphisms of $$\Lambda$$ are generated by permutations and the ordered injections $$s_{i}^{k}: \mathbf{k}-\mathbf{1} \rightarrow \mathbf{k}$$ that skip $$i$$ for $$1 \leq i \leq k .$$ It is a symmetric monoidal category with wedge sum as the symmetric monoidal product. Let $$(\mathscr{V}, \otimes, \mathcal{I})$$ be a bicomplete symmetric monoidal category with initial object $$\varnothing$$, terminal object $$*$$.

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