Timeline for What is the universal property of associated graded?

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Nov 1 at 10:59	comment	added	Nicolas Schmidt		Yes, you're right, that's an easier way to think about it: Day convolution corresponds to the graded tensor product of $k[t]$-modules, and the adjunction is the base change/restriction of scalar adjunction induced by the augmentation $k[t] \rightarrow k$.
Oct 30 at 22:03	comment	added	Daniel Teixeira		Under this definition, the category of filtered vector spaces is equivalent to the category of graded k[t]-modules through the Rees module construction. Then the adjunction in this answer corresponds to an adjunction $k[t]$-grmod $\leftrightarrows$ $k$-grmod which resembles the associated graded construction.
Jan 3, 2016 at 18:56	comment	added	LSpice		The definition of Day convolution that I turned up, via ncatlab, is intimidating. Is it the same as declaring $(V \otimes W)_i = \sum_{j + k = i} V_j \otimes W_k$, and letting the map $(V \otimes W)_i$ to $(V \otimes W)_{i + 1}$ send $V_j \otimes W_k$ to $V_{j + 1} \otimes W_k + V_j \otimes W_{k + 1}$? I guess that it must be more than that, because the sums I am writing seem only to make sense when the tensor products live in some common space, which we are explicitly avoiding assuming.
Mar 29, 2015 at 22:06	history	answered	Nicolas Schmidt	CC BY-SA 3.0