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If we have a ''monoidal category'' - a category <math>C</math> with a bifunctor <math>\otimes: C\ti ...he monoidal structure of a category. This makes the category a ''cartesian monoidal category''.

<td>lax monoidal functor</td>

This change was made to be consistent with referring to the monoidal parameter as a "query" rather than an "annotation". Simply change <code>An

== §6.4 Other monoidal classes ==

...id objects in an arbitrary [http://en.wikipedia.org/wiki/Monoidal_category monoidal category]. Such categories have a tensor product <math>\otimes</math> of ob A monoid object in a monoidal category is then:

...parenthesization is used (yes, just like in folding a list of any type of monoidal values).

...a functor <math>U:OOC\to Monoid</math> by <math>U(C) = C_1</math> with the monoidal structure on <math>U(C)</math> given by the composition in <math>C</math>. ...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

...resort the input arguments, thus including the symmetrizer of a symmetric monoidal category in the entire definition.

...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

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,