List questions from examples-counterexamples

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Identity about a Functor

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Two categories sharing the same objects and morphisms

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Associativity of concatenation of closed curves from $I$ to some topological spaces $X$

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Applications of Eckmann–Hilton argument

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Functions $\mathbb{N} \to \mathbb{N}$ that are injective but not surjective, and vice versa

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List Question

Primality test for $N=2\cdot 3^n-1$

Identity about a Functor

Two categories sharing the same objects and morphisms

Is the symmetric algebra direct sum of $k$-th symmetric powers?

Associativity of concatenation of closed curves from $I$ to some topological spaces $X$

Construct an example of a 4×4 matrix, with one of its eigenvalues equal to −3, that is not diagonal or invertible, but is diagonalizable

Example of a subgroup that is not normal (not involving permutations)

Applications of Eckmann–Hilton argument

What would be an example of free module such that cardinality of linearly independent set is greater than the rank?

Functions $\mathbb{N} \to \mathbb{N}$ that are injective but not surjective, and vice versa

Counterexample to exactness of functor from group representations to fixed points

Non-Hausdorff space such that all connected components are singletons

Examples for 1d finite element method

Example of a function such that iterated integrals are equal

Continuity and interior

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