# Search results

• ...parenthesization is used (yes, just like in folding a list of any type of monoidal values).
5 KB (788 words) - 05:52, 26 April 2021
• 11 KB (1,895 words) - 19:00, 18 May 2020
• class Functor f => Monoidal f where {{note|In category-theory speak, we say <code>f</code> is a ''lax'' monoidal functor because there aren't necessarily functions in the other direction,
179 KB (29,507 words) - 20:17, 23 July 2021
• ...a functor $U:OOC\to Monoid$ by $U(C) = C_1$ with the monoidal structure on $U(C)$ given by the composition in $C$. ...takes a one-object category and builds a monoid. Both functors respect the monoidal structures - yet these are not an isomorphism pair. The clou here is that o
19 KB (3,419 words) - 01:21, 8 October 2009
• ...monoid as all strings of some alphabet, with concatenation of strings the monoidal operation. And recall how we defined the free category on a graph as the ca
17 KB (3,008 words) - 19:19, 3 November 2009
• If we have a ''monoidal category'' - a category $C$ with a bifunctor $\otimes: C\ti ...he monoidal structure of a category. This makes the category a ''cartesian monoidal category''. 12 KB (2,218 words) - 19:16, 4 November 2009 • ...resort the input arguments, thus including the symmetrizer of a symmetric monoidal category in the entire definition. 16 KB (2,852 words) - 15:45, 22 November 2009 • <td>lax monoidal functor</td> 4 KB (677 words) - 10:52, 24 May 2010 • ...id objects in an arbitrary [http://en.wikipedia.org/wiki/Monoidal_category monoidal category]. Such categories have a tensor product [itex]\otimes$ of ob A monoid object in a monoidal category is then:
13 KB (2,245 words) - 15:18, 6 February 2021
• == ยง6.4 Other monoidal classes ==
7 KB (1,030 words) - 17:47, 18 August 2014
• This change was made to be consistent with referring to the monoidal parameter as a "query" rather than an "annotation". Simply change <code>An
3 KB (570 words) - 03:31, 6 March 2012