---
date: 2021-10-13
tags: [ web/quick-notes ]
---

# 2021-10-13

## 00:18


- A bit on [lambda sequences](lambda%20sequences) : 
	- Let $\Lambda$ be the category of based [finite sets](Finset.md) $\mathbf{n}=\{0,1,2, \cdots, n\}$ 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](symmetric%20monoidal%20category) 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 $*$.

![](figures/2021-10-13_00-19-05.png)