Question

What conditions does a functor $F: C\longrightarrow D$ need to satisfy such that its image is a subcategory of $D$?

score 73 · Answer 1 · 2019-06-08 21:30:01

73

Views

What conditions does a functor $F: C\longrightarrow D$ need to satisfy such that its image is a subcategory of $D$?

Published on 08 Jun 2019 - 21:30

score 212 · Answer 2 · 2026-03-25 04:37:46

212

Views

What structure do natural isomorphisms preserve?

Published on 25 Mar 2026 - 4:37

score 139 · Answer 3 · 2026-03-25 09:23:46

139

Views

Derived functor for of a projective module.

Published on 25 Mar 2026 - 9:23

score 595 · Answer 4 · 2026-03-25 09:28:26

595

Views

Does the vanishing of the first derived functor really imply a functor is exact?

Published on 25 Mar 2026 - 9:28

score 77 · Answer 5 · 2026-03-25 13:05:07

77

Views

Can there be nonisomorphic functorial Serre spectral sequences?

Published on 25 Mar 2026 - 13:05

score 84 · Answer 6 · 2026-03-25 01:35:29

84

Views

Defining $Hom(f,W)$

Published on 25 Mar 2026 - 1:35

score 126 · Answer 7 · 2019-06-20 04:44:40

126

Views

Why is it a consequence of a notational choice that left actions are covariant functors?

Published on 20 Jun 2019 - 4:44

score 235 · Answer 8 · 2019-06-21 04:26:57

235

Views

Understanding full and faithful functors

Published on 21 Jun 2019 - 4:26

score 49 · Answer 9 · 2019-06-21 04:47:24

49

Views

Characterizing functors $\mathscr A\times\mathscr B\to\mathscr C$

Published on 21 Jun 2019 - 4:47

score 751 · Answer 10 · 2019-06-24 21:30:05

751

Views

The image of a functor need not be a subcategory

Published on 24 Jun 2019 - 21:30

score 175 · Answer 11 · 2026-03-25 07:51:07

175

Views

On the proof that $1_{\textbf{Set}}$ is representable

Published on 25 Mar 2026 - 7:51

score 88 · Answer 12 · 2019-06-30 19:11:31

88

Views

A claim about a family of arrows forming a natural isomorphism

Published on 30 Jun 2019 - 19:11

score 73 · Answer 13 · 2019-06-30 22:40:07

73

Views

Confusion about the functoriality of $H_A:\mathscr A^{op}\to \mathbf{Set}$

Published on 30 Jun 2019 - 22:40

score 49 · Answer 14 · 2019-07-01 01:02:00

49

Views

Showing that $\mathscr P(A)\cong H_2(A)$ naturally in $A$

Published on 01 Jul 2019 - 1:02

score 464 · Answer 15 · 2019-07-01 01:18:01

464

Views

Why didn't dualization reverse all arrows in this case?

Published on 01 Jul 2019 - 1:18

List Question

What conditions does a functor $F: C\longrightarrow D$ need to satisfy such that its image is a subcategory of $D$?

What structure do natural isomorphisms preserve?

Derived functor for of a projective module.

Does the vanishing of the first derived functor really imply a functor is exact?

Can there be nonisomorphic functorial Serre spectral sequences?

Defining $Hom(f,W)$

Why is it a consequence of a notational choice that left actions are covariant functors?

Understanding full and faithful functors

Characterizing functors $\mathscr A\times\mathscr B\to\mathscr C$

The image of a functor need not be a subcategory

On the proof that $1_{\textbf{Set}}$ is representable

A claim about a family of arrows forming a natural isomorphism

Confusion about the functoriality of $H_A:\mathscr A^{op}\to \mathbf{Set}$

Showing that $\mathscr P(A)\cong H_2(A)$ naturally in $A$

Why didn't dualization reverse all arrows in this case?

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