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3. Consider a category N having only one object, let's call it *, and with one arrow n: ** for every natural number. Moreover, suppose that the composition of two arrows m and n is given by addition, that is, mon = m + n. What is the natural number n that correspond to id*: * → *? Check that the three axioms of composition are satisfied.

3. Consider a category N having only one object, let's call it *, and with one arrow n: ** for every natural number. Moreover, suppose that the composition of two arrows m and n is given by addition, that is, mon = m + n. What is the natural number n that correspond to id*: * → *? Check that the three axioms of composition are satisfied.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Exercise 3: Category Composition** Consider a category \(\mathcal{N}\) having only one object, denoted as \(*\), and with an arrow \(n: * \rightarrow *\) for every natural number. Moreover, suppose that the composition of two arrows \(m\) and \(n\) is defined by addition, i.e., \(m \circ n = m + n\). **Problem:** Determine the natural number \(n\) that corresponds to the identity arrow \(id_*: * \rightarrow *\). Verify that the three axioms of composition are satisfied.
Transcribed Image Text:**Exercise 3: Category Composition** Consider a category \(\mathcal{N}\) having only one object, denoted as \(*\), and with an arrow \(n: * \rightarrow *\) for every natural number. Moreover, suppose that the composition of two arrows \(m\) and \(n\) is defined by addition, i.e., \(m \circ n = m + n\). **Problem:** Determine the natural number \(n\) that corresponds to the identity arrow \(id_*: * \rightarrow *\). Verify that the three axioms of composition are satisfied.
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