---
date: 2021-10-02
tags: [ web/quick-notes ]
---


# 2021-10-02

## 00:20

Tags:
#personal/idle-thoughts 

Idk this weird thing

\begin{tikzcd}
	&& {A_1} && {A_2} && {A_3} &&&& {\in \mathsf{TopGrp}} \\
	\\
	\cdots && {\mathsf{B}A_1} && {\mathsf{B}A_2} && {\mathsf{B}A_3} &&&& {\in \mathsf{Top}} \\
	\\
	\cdots && {\Sigma_+^\infty \mathsf{B}A_1} && {\Sigma_+^\infty \mathsf{B}A_2} && {\Sigma_+^\infty \mathsf{B}A_3} &&&& {\mathsf{SHC}} \\
	\\
	\cdots && {[\Sigma_+^\infty \mathsf{B}A_1, E]} && {[\Sigma_+^\infty \mathsf{B}A_2, E]} && {[\Sigma_+^\infty \mathsf{B}A_3, E]} &&&& {\mathsf{SHC}} \\
	\\
	&& {\pi_*[\Sigma_+^\infty \mathsf{B}A_1, E]} && {\pi_*[\Sigma_+^\infty \mathsf{B}A_2, E]} && {\pi_*[\Sigma_+^\infty \mathsf{B}A_3, E]} &&&& {\mathsf{gradedGrp}}
	\arrow[from=3-3, to=3-5]
	\arrow[from=3-5, to=3-7]
	\arrow[from=1-3, to=1-5]
	\arrow[from=1-5, to=1-7]
	\arrow["{\mathsf{B}(\cdot)}", from=1-11, to=3-11]
	\arrow["{\Sigma_+^\infty (\cdot)}", from=3-11, to=5-11]
	\arrow[from=5-3, to=5-5]
	\arrow[from=5-5, to=5-7]
	\arrow["{[(\cdot), E]}", from=5-11, to=7-11]
	\arrow[from=7-3, to=7-5]
	\arrow[from=7-5, to=7-7]
	\arrow[from=7-1, to=7-3]
	\arrow[from=3-1, to=3-3]
	\arrow[from=5-1, to=5-3]
	\arrow["{\pi_*(\cdot)}", from=7-11, to=9-11]
	\arrow[from=9-5, to=9-7]
	\arrow[from=9-3, to=9-5]
\end{tikzcd}

> [Link to diagram](https://q.uiver.app/?(q=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))