Question

When dealing with tensor products, is it necessary to check the morphisms are well defined?

score 219 · Answer 1 · 2017-03-10 19:05:30

219

Views

When dealing with tensor products, is it necessary to check the morphisms are well defined?

Published on 10 Mar 2017 - 19:05

score 313 · Answer 2 · 2017-03-14 23:57:40

313

Views

Show two nonzero vectors $v$ and $w$ have the property $v\otimes w=w\otimes v$ iff there is $\lambda$ such that $v=\lambda w$

Published on 14 Mar 2017 - 23:57

score 171 · Answer 3 · 2017-03-15 14:56:53

171

Views

Tensor product classifies cooperating arrows?

Published on 15 Mar 2017 - 14:56

score 339 · Answer 4 · 2017-03-16 08:41:18

339

Views

In what sense is the kernel of a group homomorphism a universal arrow in a comma category?

Published on 16 Mar 2017 - 8:41

score 3.3k · Answer 5 · 2017-03-16 08:50:37

3.3k

Views

What is a Universal Construction in Category Theory?

Published on 16 Mar 2017 - 8:50

score 328 · Answer 6 · 2017-03-28 03:21:26

328

Views

Grothendieck Group - why not the free abelian group?

Published on 28 Mar 2017 - 3:21

score 352 · Answer 7 · 2017-04-04 06:27:33

352

Views

Group Presentation - Categorical Interpretation

Published on 04 Apr 2017 - 6:27

score 100 · Answer 8 · 2017-04-05 17:16:06

100

Views

Once we've prove the existence, do we really need to prove the uniqueness (of that map) in order to use the universal property?

Published on 05 Apr 2017 - 17:16

score 84 · Answer 9 · 2023-02-06 14:45:56

84

Views

Question about the meaning of a "region" in mathemathics.

Published on 06 Feb 2023 - 14:45

score 127 · Answer 10 · 2026-03-25 18:16:16

127

Views

In category theory, does a definition via a universal property induce a functor?

Published on 25 Mar 2026 - 18:16

score 273 · Answer 11 · 2026-03-25 14:42:42

273

Views

Does the direct sum have a universal property in the category of groups?

Published on 25 Mar 2026 - 14:42

score 138 · Answer 12 · 2023-03-26 08:53:07

138

Views

Universal property of multilinear maps (how to make them a tensor product)

Published on 26 Mar 2023 - 8:53

score 56 · Answer 13 · 2023-03-27 01:04:05

56

Views

Is this the correct formulation for the universal property and pushout diagram for cokernel?

Published on 27 Mar 2023 - 1:04

score 121 · Answer 14 · 2023-04-04 06:42:34

121

Views

Is there any way to prove$\{v_i \otimes w_j\}$ (with$(i,j) \in I \times J)$are basis for tensor product without using universal property?

Published on 04 Apr 2023 - 6:42

score 47 · Answer 15 · 2023-04-26 15:37:05

47

Views

How to derive this from the universal property of the ring of fractions?

Published on 26 Apr 2023 - 15:37

List Question

When dealing with tensor products, is it necessary to check the morphisms are well defined?

Show two nonzero vectors $v$ and $w$ have the property $v\otimes w=w\otimes v$ iff there is $\lambda$ such that $v=\lambda w$

Tensor product classifies cooperating arrows?

In what sense is the kernel of a group homomorphism a universal arrow in a comma category?

What is a Universal Construction in Category Theory?

Grothendieck Group - why not the free abelian group?

Group Presentation - Categorical Interpretation

Once we've prove the existence, do we really need to prove the uniqueness (of that map) in order to use the universal property?

Question about the meaning of a "region" in mathemathics.

In category theory, does a definition via a universal property induce a functor?

Does the direct sum have a universal property in the category of groups?

Universal property of multilinear maps (how to make them a tensor product)

Is this the correct formulation for the universal property and pushout diagram for cokernel?

Is there any way to prove$\{v_i \otimes w_j\}$ (with$(i,j) \in I \times J)$are basis for tensor product without using universal property?

How to derive this from the universal property of the ring of fractions?

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