- in
counit here is not
consistent with the
terminology of
limits and colimits,
because a
colimit satisfies an
initial property whereas the
counit morphisms...
- the map Δ is
called the
comultiplication (or coproduct) of C and ε is the
counit of C. Take an
arbitrary set S and form the K-vector
space C = K(S) with...
-
particularly nice,
since the
existence of
compatible comultiplication,
counit, and
antipode allows for the
construction of
tensor products of representations...
-
adjunction can be
described by its
counit and unit
natural transformations.
Using the
notation from the
previous section, the
counit ε:FG→1C{\displaystyle \varepsilon...
-
compatible with a few more axioms. Specifically, the
comultiplication and the
counit are both
unital algebra homomorphisms, or equivalently, the multiplication...
- \Delta :T^{m}V\to \bigoplus _{k=0}^{m}T^{k}V\boxtimes T^{(m-k)}V} The
counit ϵ:TV→K{\displaystyle \epsilon :TV\to K} is
given by the
projection of the...
- → T) → W T
extend and
counit must also
satisfy duals of the
monad laws:
counit ∘ ( (wa =>> f) → wb ) ↔ f(wa) → b wa =>>
counit ↔ wa wa ( (=>> f(wx = wa))...
- ϵ:A→K{\displaystyle \epsilon :A\to K} (corresponding to trace,
called the
counit). The
composition ϵ∘η:K→K{\displaystyle \epsilon \circ \eta :K\to K} is...
-
using the
counit map of the adjunction: T2=G∘F∘G∘F→G∘
counit∘FG∘F=T.{\displaystyle T^{2}=G\circ F\circ G\circ F\xrightarrow {G\circ {\text{
counit}}\circ F}...
- and
Superman In mathematics, the
coidentity of a dual
group object or the
counit of a
coalgebra In sociology,
double consciousness This
disambiguation page...