Question

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

score 49 · Answer 1 · 2026-04-28 15:35:09

49

Views

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

Published on 28 Apr 2026 - 15:35

score 194 · Answer 2 · 2026-04-23 01:31:50

194

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 23 Apr 2026 - 1:31

score 66 · Answer 3 · 2026-04-29 10:44:57

66

Views

Sandwich natural transformation between two functors

Published on 29 Apr 2026 - 10:44

score 519 · Answer 4 · 2026-05-10 14:48:29

519

Views

What is an algebra over a monad?

Published on 10 May 2026 - 14:48

score 151 · Answer 5 · 2026-04-26 15:32:42

151

Views

Model category of all model categories

Published on 26 Apr 2026 - 15:32

score 74 · Answer 6 · 2026-05-01 15:57:04

74

Views

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

Published on 01 May 2026 - 15:57

score 1.5k · Answer 7 · 2026-05-10 20:39:26

1.5k

Views

Product in the category of functors.

Published on 10 May 2026 - 20:39

score 44 · Answer 8 · 2026-04-12 22:45:35

44

Views

Relation between functors under an equivalence

Published on 12 Apr 2026 - 22:45

score 397 · Answer 9 · 2026-04-15 13:23:03

397

Views

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

Published on 15 Apr 2026 - 13:23

score 157 · Answer 10 · 2026-04-17 10:06:34

157

Views

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

Published on 17 Apr 2026 - 10:06

score 208 · Answer 11 · 2026-04-15 03:11:33

208

Views

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

Published on 15 Apr 2026 - 3:11

score 64 · Answer 12 · 2026-05-10 15:55:04

64

Views

Join of simplicial sets induces a functor.

Published on 10 May 2026 - 15:55

score 111 · Answer 13 · 2026-05-10 14:49:20

111

Views

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

Published on 10 May 2026 - 14:49

score 90 · Answer 14 · 2026-05-10 14:56:17

90

Views

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

Published on 10 May 2026 - 14:56

score 251 · Answer 15 · 2026-05-10 16:14:41

251

Views

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

Published on 10 May 2026 - 16:14

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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