Is there a product of chain complex?

Asked Sep 20 '21 at 11:55

Active Sep 20 '21 at 11:55

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In the Cup_product article of Wikipedia:

It is possible to view the cup product as induced from the following composition: $$C^\bullet(X)\times C^\bullet(X)\to C^\bullet(X\times X)\overset{\Delta^*}\to C^\bullet(X)$$

How is $C^\bullet(X)\times C^\bullet(X)$ defined? Is it just a typo for $C^\bullet(X)\otimes C^\bullet(X)$?

asked Sep 20 '21 at 11:55

jw_

Yes for consistency and you might actually also want to put in the explicit $\operatorname{Tot}$ too just in case you also use $\otimes$ to get a double complex. – user10354138 Sep 20 '21 at 12:36
@user10354138 What is Tot and what did you mean? – jw_ Sep 23 '21 at 10:36
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Total complex of a double complex. – user10354138 Sep 23 '21 at 11:53

Is there a product of chain complex?

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