Definition of Counit. Meaning of Counit. Synonyms of Counit

Here you will find one or more explanations in English for the word Counit. Also in the bottom left of the page several parts of wikipedia pages related to the word Counit and, of course, Counit synonyms and on the right images related to the word Counit.

Definition of Counit

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Meaning of Counit from wikipedia

- 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...