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8 Bialgebroids as algebroids with more structure
 8.1 Properties
 8.2 Attributes
 8.3 Constructors
 8.4 GAP categories

8 Bialgebroids as algebroids with more structure

8.1 Properties

8.1-1 IsCocommutative
‣ IsCocommutative( B )( property )

Returns: true or false

Check whether the bialgebroid B is cocommutative.

8.1-2 IsHopfAlgebroid
‣ IsHopfAlgebroid( B )( property )

Returns: true or false

Check whether the antipode of B is actually an antipode.

8.2 Attributes

8.2-1 Counit
‣ Counit( B )( attribute )

Returns: a CAP functor

The counit of the bialgebroid B.

8.2-2 Comultiplication
‣ Comultiplication( B )( attribute )

Returns: a CAP functor

The comultiplication of the bialgebroid B.

8.3 Constructors

8.3-1 AddBialgebroidStructure
‣ AddBialgebroidStructure( A, counit, comult )( operation )

Returns: a CAP category

Add to the algebroid A a counit and a comultiplication using the defining records counit and comult, respectively.

8.3-2 AddAntipode
‣ AddAntipode( B, S )( operation )

Returns: a CAP category

Add to the bialgebroid B an antipode S.

8.4 GAP categories

8.4-1 IsBialgebroid
‣ IsBialgebroid( arg )( filter )

Returns: true or false

The GAP category of bialgebroids.

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