List questions from natural-transformations

130

Views

A natural isomorphism $\mathsf C(\operatorname{colim} F, Y) \cong \lim \mathsf C(F-, Y)$. Understanding $\lim$ as a functor?

Published on 24 Mar 2026 - 5:03

52

Views

Definition of an algebra over a monad by using equalities between natural transformations

Published on 24 Mar 2026 - 23:45

76

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Square of unit in a monoidal category

Published on 22 Mar 2026 - 1:39

182

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Change scores/difference scores on a logarithmic scale

Published on 24 Aug 2021 - 6:58

192

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Is the standard isomorphism $L(F^n,F^n)\to F^{n\times n}$ a natural transformation?

Published on 01 Sep 2021 - 17:31

94

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Why $\Psi\circ\Phi=1$ in Yoneda lemma?

Published on 08 Sep 2021 - 10:10

176

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$n$-Simplices of Fiber product of Simplicial sets

Published on 07 Oct 2021 - 23:03

254

Views

Natural Transformation of Bifunctors

Published on 16 Oct 2021 - 19:55

61

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Morphism between free abelian groups is 1-1; Vick Prop. 1.9

Published on 25 Mar 2026 - 19:16

135

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Natural transformations of the identity functor

Published on 05 Dec 2021 - 12:09

220

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Any two natural transformations between identity functors commute

Published on 13 Dec 2021 - 1:52

79

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In what sense is the uniqueness of left adjoint isomorphism 'canonical'

Published on 16 Dec 2021 - 10:07

79

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Is natural isomorphism unique？

Published on 26 Dec 2021 - 9:04

189

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Isomorphism not natural in $X$?

Published on 29 Dec 2021 - 20:30

36

Views

Do (special) natural transformations imply a commutative triangle of functors (but NOT vice versa)?

Published on 10 Mar 2022 - 16:47

List Question

A natural isomorphism $\mathsf C(\operatorname{colim} F, Y) \cong \lim \mathsf C(F-, Y)$. Understanding $\lim$ as a functor?

Definition of an algebra over a monad by using equalities between natural transformations

Square of unit in a monoidal category

Change scores/difference scores on a logarithmic scale

Is the standard isomorphism $L(F^n,F^n)\to F^{n\times n}$ a natural transformation?

Why $\Psi\circ\Phi=1$ in Yoneda lemma?

$n$-Simplices of Fiber product of Simplicial sets

Natural Transformation of Bifunctors

Morphism between free abelian groups is 1-1; Vick Prop. 1.9

Natural transformations of the identity functor

Any two natural transformations between identity functors commute

In what sense is the uniqueness of left adjoint isomorphism 'canonical'

Is natural isomorphism unique？

Isomorphism not natural in $X$?

Do (special) natural transformations imply a commutative triangle of functors (but NOT vice versa)?

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