Question

Non-natural transformation example

score 616 · Answer 1 · 2026-03-21 21:04:40

616

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Non-natural transformation example

Published on 21 Mar 2026 - 21:04

score 1.4k · Answer 2 · 2026-03-23 12:00:13

1.4k

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What intuitive notion is formalized by "natural transformation" in category theory?

Published on 23 Mar 2026 - 12:00

score 306 · Answer 3 · 2026-03-25 02:18:23

306

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understanding natural transformations that are not natural isomorphisms

Published on 25 Mar 2026 - 2:18

score 77 · Answer 4 · 2026-03-16 21:40:26

77

Views

Proving for two naturally isomorphic functors, if one is full, then so is the other.

Published on 16 Mar 2026 - 21:40

score 364 · Answer 5 · 2026-03-17 10:34:02

364

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Showing when two functors are naturally isomorphic, if one is faithful, then the other also is.

Published on 17 Mar 2026 - 10:34

score 106 · Answer 6 · 2026-03-17 13:54:49

106

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Proving equivalent categories have binary products if one of them does

Published on 17 Mar 2026 - 13:54

score 43 · Answer 7 · 2026-03-16 22:29:57

43

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How to arrive at unique factorization through the limit given naturality compatibility conditions?

Published on 16 Mar 2026 - 22:29

score 189 · Answer 8 · 2026-03-16 23:17:29

189

Views

If the Yoneda lemma essentially says that $\text{Hom}(\text{Hom}(\cdot, x), A) \simeq A(x)$, then what about higher iterates of $\text{Hom}$?

Published on 16 Mar 2026 - 23:17

score 59 · Answer 9 · 2026-03-22 19:11:46

59

Views

Sandwich natural transformation between two functors

Published on 22 Mar 2026 - 19:11

score 67 · Answer 10 · 2026-03-17 05:24:07

67

Views

$[\mathsf{I},\mathsf{C}]$ and $[\mathsf{J},\mathsf{C}]$ are equivalent if $\mathsf{I}$ and $\mathsf{J}$ are.

Published on 17 Mar 2026 - 5:24

score 44 · Answer 11 · 2026-03-22 19:53:44

44

Views

Every natural isomorphism decomposes through another

Published on 22 Mar 2026 - 19:53

score 1.5k · Answer 12 · 2026-03-25 03:02:35

1.5k

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Product in the category of functors.

Published on 25 Mar 2026 - 3:02

score 439 · Answer 13 · 2026-03-25 03:01:17

439

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Riehl's "Category Theory in Context" - Exercise 3.4.i

Published on 25 Mar 2026 - 3:01

score 111 · Answer 14 · 2026-03-25 03:07:21

111

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Proving adjoint equivalence from natural isomorphic unit

Published on 25 Mar 2026 - 3:07

score 246 · Answer 15 · 2026-03-25 03:03:49

246

Views

How is it obvious that $\times : C \times C \to C$ is right adjoint to the diagonal functor?

Published on 25 Mar 2026 - 3:03

List Question

Non-natural transformation example

What intuitive notion is formalized by "natural transformation" in category theory?

understanding natural transformations that are not natural isomorphisms

Proving for two naturally isomorphic functors, if one is full, then so is the other.

Showing when two functors are naturally isomorphic, if one is faithful, then the other also is.

Proving equivalent categories have binary products if one of them does

How to arrive at unique factorization through the limit given naturality compatibility conditions?

If the Yoneda lemma essentially says that $\text{Hom}(\text{Hom}(\cdot, x), A) \simeq A(x)$, then what about higher iterates of $\text{Hom}$?

Sandwich natural transformation between two functors

$[\mathsf{I},\mathsf{C}]$ and $[\mathsf{J},\mathsf{C}]$ are equivalent if $\mathsf{I}$ and $\mathsf{J}$ are.

Every natural isomorphism decomposes through another

Product in the category of functors.

Riehl's "Category Theory in Context" - Exercise 3.4.i

Proving adjoint equivalence from natural isomorphic unit

How is it obvious that $\times : C \times C \to C$ is right adjoint to the diagonal functor?

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