4
votes
0answers
138 views

Injectivity criterion for surjective coalgebra maps: does it hold in full generality?

Let $k$ be a commutative ring. Let $C$ be a filtered $k$-coalgebra. This means a $k$-coalgebra equipped with an increasing $k$-module filtration $C^0 \subseteq C^1 \subseteq C^2 \subseteq ...$ ...
0
votes
3answers
949 views

How to work with co-multiplication?

Let $C$ be a coalgebra and $\Delta: C \to C\otimes C$ a co-multiplication map. Then, due the co-associative property we can consider $\Delta^m$. But how is defined $\Delta^{m}: C \to C^{\otimes m}$??? ...