Question

Bijection between $\textbf{Cat}(A \times B, C)$ and $\textbf{Cat}(A, C^B)$: Mac Lane Exercise 1 Chapter II section 5

score 113 · Answer 1 · 2026-03-25 10:55:52

113

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Bijection between $\textbf{Cat}(A \times B, C)$ and $\textbf{Cat}(A, C^B)$: Mac Lane Exercise 1 Chapter II section 5

Published on 25 Mar 2026 - 10:55

score 211 · Answer 2 · 2026-05-10 13:50:17

211

Views

Promoting equivalence to adjoint equivalence: explicit construction of a unit and a counit

Published on 10 May 2026 - 13:50

score 474 · Answer 3 · 2026-03-25 10:57:14

474

Views

Proving that the horizontal composition of natural transformations is a natural transformation

Published on 25 Mar 2026 - 10:57

score 56 · Answer 4 · 2026-03-25 10:55:37

56

Views

Dinatural isomorphism from tangent functor to cotangent functor

Published on 25 Mar 2026 - 10:55

score 71 · Answer 5 · 2026-04-23 09:01:58

71

Views

Why unnatural isomorphisms are not mathematically well- behaved?

Published on 23 Apr 2026 - 9:01

score 63 · Answer 6 · 2026-03-26 16:07:43

63

Views

Natural transformation induced by adjoint functors.

Published on 26 Mar 2026 - 16:07

score 310 · Answer 7 · 2026-05-02 22:19:43

310

Views

Trouble understanding what a natural transformation is

Published on 02 May 2026 - 22:19

score 112 · Answer 8 · 2026-04-08 20:30:33

112

Views

Extension of Scalars is a pseudofunctor

Published on 08 Apr 2026 - 20:30

score 358 · Answer 9 · 2026-04-27 17:22:58

358

Views

Riehl's Category Theory in Context - Exercise 1.5.vii without Axiom of Choice

Published on 27 Apr 2026 - 17:22

score 141 · Answer 10 · 2026-04-18 09:00:30

141

Views

Not all Monads are Idempotent, a Cautionary Tale on Natural Transformations

Published on 18 Apr 2026 - 9:00

score 49 · Answer 11 · 2026-04-15 21:42:43

49

Views

Naturality of certain isomorphisms for $\mathrm{Hom}$-functors

Published on 15 Apr 2026 - 21:42

score 256 · Answer 12 · 2026-04-18 19:03:03

256

Views

Cisinski, Higher Categories and Homotopical Algebra, Theorem 1.1.10

Published on 18 Apr 2026 - 19:03

score 321 · Answer 13 · 2026-04-19 00:09:18

321

Views

Describing a natural transformation in terms of hom-sets.

Published on 19 Apr 2026 - 0:09

score 155 · Answer 14 · 2026-04-23 01:46:20

155

Views

Adjoints of two naturally isomorphic functors

Published on 23 Apr 2026 - 1:46

score 295 · Answer 15 · 2026-04-23 06:10:08

295

Views

Natural transformations as categorical homotopies

Published on 23 Apr 2026 - 6:10

List Question

Bijection between $\textbf{Cat}(A \times B, C)$ and $\textbf{Cat}(A, C^B)$: Mac Lane Exercise 1 Chapter II section 5

Promoting equivalence to adjoint equivalence: explicit construction of a unit and a counit

Proving that the horizontal composition of natural transformations is a natural transformation

Dinatural isomorphism from tangent functor to cotangent functor

Why unnatural isomorphisms are not mathematically well- behaved?

Natural transformation induced by adjoint functors.

Trouble understanding what a natural transformation is

Extension of Scalars is a pseudofunctor

Riehl's Category Theory in Context - Exercise 1.5.vii without Axiom of Choice

Not all Monads are Idempotent, a Cautionary Tale on Natural Transformations

Naturality of certain isomorphisms for $\mathrm{Hom}$-functors

Cisinski, Higher Categories and Homotopical Algebra, Theorem 1.1.10

Describing a natural transformation in terms of hom-sets.

Adjoints of two naturally isomorphic functors

Natural transformations as categorical homotopies

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