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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"
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 ...
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.
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 ...
Monoidal categories can be seen as a generalization of these and other examples. Every ( small ) monoidal category may also be viewed as a " categorification " of an underlying monoid , namely the monoid whose elements are the isomorphism classes of the category's objects and whose binary operation is given by the category's tensor product.
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.
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.
Initiation of translation in bacteria involves the assembly of the components of the translation system, which are: the two ribosomal subunits (50S and 30S subunits); the mature mRNA to be translated; the tRNA charged with N-formylmethionine (the first amino acid in the nascent peptide); guanosine triphosphate (GTP) as a source of energy, and the three prokaryotic initiation factors IF1, IF2 ...