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- In Set, why are projections not epic but injections are monic?
That’s why the embeddings into the coproduct are always monic (always being injective, even in the degenerate case of an empty cofactor) but the projections are not always epic (because they may not be surjective in the degenerate case of an empty factor)
- category theory - Monic $\iff$ every component is monic? - Mathematics . . .
Monic every component is monic? Ask Question Asked 1 month ago Modified 1 month ago
- linear algebra - Irreducible polynomials in $\mathbb F_3 [x . . .
Using the same trick as for degree 2, it is straightforward to find the irreducible monic polynomials of degree 3 Degree 4: Observe that x2 + 1 x 2 + 1 is irreducible of degree 2 2
- divisibility - Finding a gcd in the form of a monic polynomial . . .
Similarly, in your example, for polynomials over a field, we may normalize gcds by scaling them to be monic, i e scale the polynomial by the inverse of its leading coefficient to force the lead coefficient to be 1 1
- linear algebra - Characteristic polynomial of a matrix is monic . . .
The characteristic polynomial is the product of monic degree-1 or degree-2 terms, corresponding to eigenvalues and eigenpairs, respectively The set of monic polynomials is closed under multiplication
- What do Monic and epic morphisms imply? - Mathematics Stack Exchange
Question: if you tell me a morphism is epic or monic, what other insight do I gain about the morphism that is equivalent but conceptually what we actually use? (since just taking about cancellations seems unnatural and unworthy of a name to me right now)
- Find the monic generator of and ideal. - Mathematics Stack Exchange
Find the monic generator of the ideal of all polynomials f in F[x] such that f(A) = 0
- Is the canonical morphism from $A$ to $R^{R^A}$ monic?
∂A ∂ A is not always monic Let C C be the category of sets and let R R be a one-element set Then RA R A exists and is a one-element set for all A A, so ∂A ∂ A won't be monic when A A has 2 or more elements I don't immediately see nice conditions to make ∂A ∂ A monic, though in the category of sets it would suffice to require R R to have at least two elements Intuitively, you
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