List questions from universal-property

Published on 04 Mar 2022 - 16:26

99

Views

Universal characterization of the arrow (interval, ordinal, 1-simplex) object? (Is $2$-category theory actually needed?)

Published on 11 Mar 2022 - 15:05

165

Views

Proving the universal property of subspace topology

Published on 15 Mar 2022 - 7:35

160

Views

Prove that for all rings $R$ and all $r \in R$, there exists a unique ring homomorphism $\varphi: \Bbb Z[x] \to R$ such that $\varphi(x)=r$.

Published on 15 Mar 2022 - 18:56

59

Views

Connecting Mac Lane's discussion of free categories from graphs to free algebraic systems

Published on 04 May 2022 - 18:53

278

Views

Finite product and coproduct are the same in abelian categories

Published on 12 May 2022 - 18:21

237

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Why do we require uniqueness in the universal property for a fraction field?

Published on 15 May 2022 - 5:21

140

Views

Prove: there exist a unique group homomorphism $\bar{f}: G_1/H_1 \to G_2/H_2$

Published on 29 May 2022 - 4:27

35

Views

Why $\bar{f}(x + H_1) = f(x) + H_2$?

Published on 31 May 2022 - 20:21

140

Views

Kan extensions as weighted limits

Published on 23 Feb 2026 - 8:34

38

Views

Universal Property of The Simplex Category Δop

Published on 26 Jun 2022 - 21:13

78

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Does the universal set operate as the Von Neumann universe in non well founded set theories?

Published on 27 Jun 2022 - 2:52

72

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Can fibrations be described via universal morphisms?

Published on 10 Jul 2022 - 17:16

65

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Well-definedness of tensor product of modules

Published on 11 Jul 2022 - 16:08

211

Views

Short exact sequence of pointed spaces induces isomorphism of quotients

Published on 13 Jul 2022 - 17:46

List Question

Exercise $0.11$ from Leinster's Basic Category Theory

Universal characterization of the arrow (interval, ordinal, 1-simplex) object? (Is $2$-category theory actually needed?)

Proving the universal property of subspace topology

Prove that for all rings $R$ and all $r \in R$, there exists a unique ring homomorphism $\varphi: \Bbb Z[x] \to R$ such that $\varphi(x)=r$.

Connecting Mac Lane's discussion of free categories from graphs to free algebraic systems

Finite product and coproduct are the same in abelian categories

Why do we require uniqueness in the universal property for a fraction field?

Prove: there exist a unique group homomorphism $\bar{f}: G_1/H_1 \to G_2/H_2$

Why $\bar{f}(x + H_1) = f(x) + H_2$?

Kan extensions as weighted limits

Universal Property of The Simplex Category Δop

Does the universal set operate as the Von Neumann universe in non well founded set theories?

Can fibrations be described via universal morphisms?

Well-definedness of tensor product of modules

Short exact sequence of pointed spaces induces isomorphism of quotients

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