- ****ociativity of
algebra multiplication (called the co****ociativity of the
comultiplication); the
second diagram is the dual of the one
expressing the existence...
- Hopf
algebra is
particularly nice,
since the
existence of
compatible comultiplication, counit, and
antipode allows for the
construction of
tensor products...
-
structures are made
compatible with a few more axioms. Specifically, the
comultiplication and the
counit are both
unital algebra homomorphisms, or equivalently...
-
axiom of the counit. A
bialgebra defines both multiplication, and
comultiplication, and
requires them to be compatible.
Multiplication is
given by an...
- the
lattice Primitive element (coalgebra), an
element X on
which the
comultiplication Δ has the
value Δ(X) = X⊗1 + 1⊗X
Primitive element (free group), an...
- is
dense in C;
There exists a C*-algebra
homomorphism called the
comultiplication Δ: C → C ⊗ C (where C ⊗ C is the C*-algebra
tensor product - the completion...
- Λ2(V),
where the
first map is the
comultiplication along the
first coordinate. The
other map is a
comultiplication Λ4(V) → Λ2(V) ⊗ Λ2(V). For a partition...
-
examples of *-algebras (with the
additional structure of a
compatible comultiplication); the most
familiar example being: The
group Hopf algebra: a group...
- for
various logical connectives, such as e.g.
multiplication (AND),
comultiplication (OR),
division (UN-AND) and co-division (UN-OR) of opinions, conditional...
- A{\displaystyle A}-bimodule in a
specific way. One of the
structure maps is the
comultiplication Δ:H→H⊗AH{\displaystyle \Delta :H\to H\otimes _{A}H}
which is an A{\displaystyle...
