Question

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

score 43 · Answer 1 · 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 2 · 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 3 · 2026-03-22 19:11:46

59

Views

Sandwich natural transformation between two functors

Published on 22 Mar 2026 - 19:11

score 515 · Answer 4 · 2018-11-28 06:53:29

515

Views

What is an algebra over a monad?

Published on 28 Nov 2018 - 6:53

score 136 · Answer 5 · 2026-03-23 03:10:11

136

Views

Model category of all model categories

Published on 23 Mar 2026 - 3:10

score 67 · Answer 6 · 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 1.5k · Answer 7 · 2026-03-25 03:02:35

1.5k

Views

Product in the category of functors.

Published on 25 Mar 2026 - 3:02

score 41 · Answer 8 · 2018-12-16 15:50:17

41

Views

Relation between functors under an equivalence

Published on 16 Dec 2018 - 15:50

score 394 · Answer 9 · 2018-12-18 19:35:58

394

Views

Why is $\mathbb{G}_m$ is a representable functor?

Published on 18 Dec 2018 - 19:35

score 152 · Answer 10 · 2018-12-22 15:19:46

152

Views

$\mathcal{Nil}_n$ isomorphic to $h^A$ with $A=\mathbb{Z}[x]/(x^n)$

Published on 22 Dec 2018 - 15:19

score 205 · Answer 11 · 2018-12-22 17:15:33

205

Views

checking that there is a functor $\texttt{Nil}_n: Ring \longrightarrow Set$

Published on 22 Dec 2018 - 17:15

score 60 · Answer 12 · 2018-12-25 17:35:42

60

Views

Join of simplicial sets induces a functor.

Published on 25 Dec 2018 - 17:35

score 109 · Answer 13 · 2018-12-31 12:28:25

109

Views

What does the endofunctor/monad that sends a set to the set of finite words on the set do to morphisms?

Published on 31 Dec 2018 - 12:28

score 88 · Answer 14 · 2018-12-31 14:47:31

88

Views

checking the functor $\texttt{Nil}_n$ is represented by $(\mathbb{Z}[x]/(x^n), \tau_R)$

Published on 31 Dec 2018 - 14:47

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

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

What is an algebra over a monad?

Model category of all model categories

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

Product in the category of functors.

Relation between functors under an equivalence

Why is $\mathbb{G}_m$ is a representable functor?

$\mathcal{Nil}_n$ isomorphic to $h^A$ with $A=\mathbb{Z}[x]/(x^n)$

checking that there is a functor $\texttt{Nil}_n: Ring \longrightarrow Set$

Join of simplicial sets induces a functor.

What does the endofunctor/monad that sends a set to the set of finite words on the set do to morphisms?

checking the functor $\texttt{Nil}_n$ is represented by $(\mathbb{Z}[x]/(x^n), \tau_R)$

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

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