Suppose we are given filtrations of finite dimensional vectors spaces: $$ B_d\subseteq Z_d\subseteq C_d$$ $$0 \subseteq C_{d,1} \subseteq C_d$$ $$0 \subseteq Z_{d,1} \subseteq Z_d$$ $$0 \subseteq B_{d,1} \subseteq B_d$$ Where $Z_{d,1}=Z_d\cap C_{d,1}$ and $B_{d,1}=B_d\cap C_{d,1}$. Is it true that $$\frac{\frac{Z_d}{Z_{d,1}}}{\frac{B_d}{B_{d,1}}}\cong\frac{\frac{Z_d}{B_d}}{\frac{Z_{d,1}}{B_{d,1}}}? $$
2026-03-25 06:29:21.1774420161
Quotient of quotients in finite dimensional vector spaces
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