Given a coalgebra $C$ with a filtration $F$ such that $\Delta(F^n C)\subset \sum_{i=0}^n F^i C\otimes F^{n-i} C$, how does the coproduct manifest in the associated graded? Do we get something to the effect of $\Delta(F^n C)\subset F^0 C\otimes F^{n} C + F^n C\otimes F^{0} C$?
2026-03-25 12:43:07.1774442587
The associated graded of a filtered coalgebra
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