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Function f : [Z] 3 → [Z] 6 given by [k] 3 ↦ [3k] 6 is a semigroup homomorphism, since [3k ⋅ 3l] 6 = [9kl] 6 = [3kl] 6. However, f([1] 3) = [3] 6 ≠ [1] 6, so a monoid homomorphism is a semigroup homomorphism between monoids that maps the identity of the first monoid to the identity of the second monoid and the latter condition cannot be ...
Ordinary monoids are precisely the monoid objects in the cartesian monoidal category Set. Further, any (small) strict monoidal category can be seen as a monoid object in the category of categories Cat (equipped with the monoidal structure induced by the cartesian product).
A monoid object in the category of monoids (with the direct product of monoids) is just a commutative monoid. This follows easily from the Eckmann–Hilton argument. A monoid object in the category of complete join-semilattices Sup (with the monoidal structure induced by the Cartesian product) is a unital quantale.
M. Kilp, U. Knauer, A.V. Mikhalev, Monoids, Acts and Categories with Applications to Wreath Products and Graphs, De Gruyter Expositions in Mathematics vol. 29, Walter de Gruyter, 2000, ISBN 3-11-015248-7. Ronald V. Book and Friedrich Otto, String-rewriting Systems, Springer, 1993, ISBN 0-387-97965-4, chapter 7, "Algebraic Properties"
Overview of eukaryotic messenger RNA (mRNA) translation Translation of mRNA and ribosomal protein synthesis Initiation and elongation stages of translation involving RNA nucleobases, the ribosome, transfer RNA, and amino acids The three phases of translation: (1) in initiation, the small ribosomal subunit binds to the RNA strand and the initiator tRNA–amino acid complex binds to the start ...
Translation initiation is sometimes described as three step process which initiation factors help to carry out. First, the tRNA carrying a methionine amino acid binds to the small subunit of ribosome, then binds to the mRNA , and finally joins together with the large subunit of ribosome.
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Translation is one of the key energy consumers in cells, hence it is strictly regulated. Numerous mechanisms have evolved that control and regulate translation in eukaryotes as well as prokaryotes. Regulation of translation can impact the global rate of protein synthesis which is closely coupled to the metabolic and proliferative state of a cell.