Monoidal may refer to:
*
Monoidal category
In mathematics, a monoidal category (or tensor category) is a category (mathematics), category \mathbf C equipped with a bifunctor
:\otimes : \mathbf \times \mathbf \to \mathbf
that is associative up to a natural isomorphism, and an Object (cate ...
, concept in category theory
**
Monoidal functor
In category theory, monoidal functors are functors between monoidal categories which preserve the monoidal structure. More specifically, a monoidal functor between two monoidal categories consists of a functor between the categories, along with two ...
, between monoidal categories
**
Monoidal natural transformation
Suppose that (\mathcal C,\otimes,I) and (\mathcal D,\bullet, J) are two monoidal categories and
:(F,m):(\mathcal C,\otimes,I)\to(\mathcal D,\bullet, J) and (G,n):(\mathcal C,\otimes,I)\to(\mathcal D,\bullet, J)
are two lax monoidal functors betwee ...
, between monoidal functors
*
Monoidal transformation
In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with the space of all directions pointing out of that subspace. For example, the blowup of a point in a plane replaces the poin ...
, in algebraic geometry
See also
*
Monoid
In abstract algebra, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition form a monoid, the identity element being .
Monoids are semigroups with identity ...
, an algebraic structure
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Monoid (category theory)
In category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) in a monoidal category is an object ''M'' together with two morphisms
* ''μ'': ''M'' ⊗ ''M'' → ''M'' called ''multiplication'',
* ''η ...
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