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.
- 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... - in counit here is not consistent with the terminology of limits and colimits, because a colimitsatisfies an initialpropertywhereas the counit morphisms... - adjunction can be described by its counit and unit natural transformations. Using the notation from the previous section, the counit ε : F G → 1 C {\displaystyle... - particularly nice, since the existence of compatible comultiplication, counit, and antipodeallows for the construction of tensorproducts of representations... - compatible with a few more axioms. Specifically, the comultiplication and the counit are both unitalalgebra homomorphisms, or equivalently, the multiplication... - {\displaystyle \Delta :T^{m}V\to \bigoplus _{k=0}^{m}T^{k}V\boxtimes T^{(m-k)}V} The counit ϵ : T V → K {\displaystyle \epsilon :TV\to K} is given by the projection... - K {\displaystyle \epsilon :A\to K} (corresponding to trace, called the counit). The composition ϵ ∘ η : K → K {\displaystyle \epsilon \circ \eta :K\to... - → T) → W T extend and counit must also satisfyduals of the monad laws: counit ∘ ( (wa =>> f) → wb ) ↔ f(wa) → b wa =>> counit ↔ wa wa ( (=>> f(wx = wa))... - η A : I → A ∗ ⊗ A {\displaystyle \eta _{A}:I\to A^{*}\otimes A} and the counit ε A : A ⊗ A ∗ → I {\displaystyle \varepsilon _{A}:A\otimes A^{*}\to I} ... - multiplication map is constructedusing the counit map of the adjunction: T 2 = G ∘ F ∘ G ∘ F → G ∘ counit ∘ F G ∘ F = T . {\displaystyle T^{2}=G\circ...
