Examples of 'monoidal' in a sentence
Meaning of "monoidal"
The term 'monoidal' in mathematics refers to a set equipped with a binary operation that is associative and has an identity element. It is used in the context of algebraic structures like monoids and categories
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- Of, pertaining to, or being a monoid.
How to use "monoidal" in a sentence
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monoidal
Such a category is sometimes called a cartesian monoidal category.
Special types of monoidal categories exist with interesting properties.
It is shown that a cartesian bicategory is a symmetric monoidal bicategory.
Every monoidal category is monoidally equivalent to a strict monoidal category.
A cosmos is a complete cocomplete closed symmetric monoidal category.
Monoidal categories can be seen as a generalization of these and other examples.
The coherence maps of strong monoidal functors are invertible.
Monoidal categories have numerous applications outside of category theory proper.
We obtain instead that the category of modules is monoidal closed.
A strict monoidal functor is a monoidal functor whose coherence maps are identities.
Monoids are also considered as a suitable setting for automata in monoidal categories.
Hopf monoidal comonads.
Hopf algebras can be seen as a generalization of group objects to monoidal categories.
Braided monoidal categories.
The term tensor product is also used in relation to monoidal categories.
See also
Braided monoidal category.
In fact any category with finite products can be given a monoidal structure.
We have described closed monoidal categories as monoidal categories with an extra property.
The theory of enriched categories started with enrichment over a monoidal category.
A dagger symmetric monoidal category is a symmetric monoidal category with a compatible dagger structure.
The most general setting for the tensor product is the monoidal category.
This theorem states that any monoidal category is monoidally equivalent to a strict monoidal category.
Ordinary monoids are precisely the monoid objects in the cartesian monoidal category Set.
A TQFT on M is a symmetric monoidal functor from hBordM to the category of vector spaces.
Programming in ASCII-art with monoidal categories.
Finally, the monoidal unit is a simple object.
The augmented simplex category, unlike the simplex category, admits a natural monoidal structure.
In category theory, monoidal functors are functors between monoidal categories which preserve the monoidal structure.
More precisely, Ab is a closed monoidal category.
Braided monoidal categories have applications in quantum information, quantum field theory, and string theory.
Some examples and non-examples of symmetric monoidal categories, The category of sets.
Monoidal preorders, also known as " preordered monoids ", are special cases of monoidal categories.
The category of symmetric spectra has a monoidal product denoted by ∧ { \ displaystyle \ wedge.
If, moreover, this natural isomorphism is its own inverse, we have a symmetric monoidal category.
Dually, a comonoid in a monoidal category C is a monoid in the dual category Cop.
Another basic example is to consider a 2-category with a single object ; these are essentially monoidal categories.
A blowup can also be called monoidal transformation, locally quadratic transformation, dilatation, σ-process, or Hopf map.
The ordinary tensor product makes vector spaces, abelian groups, R-modules, or R-algebras into monoidal categories.
Monoidal applicatives Scalaz implements Monoid[m]. applicative to turn any monoids into an applicative.
In particular, the category of vector spaces over a field K { \ displaystyle K } is a symmetric, closed monoidal category.
Convolution appears as the internal hom for a monoidal structure on C a t e n { \ displaystyle { \ bf { Caten.
