Question

Given a sub-presheaf $(F,\alpha)\subseteq X$, how does one create subobjects $y_{A,x}\subseteq\scr{A}$ $(\cdot,A)$ for all $(A,x)\in\int_\scr{A}$ $X$?

score 83 · Answer 1 · 2022-06-12 18:42:04

83

Views

Given a sub-presheaf $(F,\alpha)\subseteq X$, how does one create subobjects $y_{A,x}\subseteq\scr{A}$ $(\cdot,A)$ for all $(A,x)\in\int_\scr{A}$ $X$?

Published on 12 Jun 2022 - 18:42

score 139 · Answer 2 · 2022-06-13 07:47:15

139

Views

To prove $ \Bbb{Z}_p$ is isomorphic to $\lim_{←}\Bbb{Z}_p/p^n \Bbb{Z}_p$ as a ring

Published on 13 Jun 2022 - 7:47

score 253 · Answer 3 · 2026-03-26 21:27:25

253

Views

Is there a simple abstract reason why a profinite group is an inverse limit of finite groups?

Published on 26 Mar 2026 - 21:27

score 41 · Answer 4 · 2022-06-23 11:18:28

41

Views

Symmetry of colimits

Published on 23 Jun 2022 - 11:18

score 150 · Answer 5 · 2022-06-25 13:57:37

How necessary is the filteredness condition in the result “a filtered diagram in which all morphisms are isomorphisms has a colimit”?

score 685 · Answer 6 · 2026-03-28 16:14:28

685

Views

Definition of Limits in Category Theory

Published on 28 Mar 2026 - 16:14

score 70 · Answer 7 · 2022-07-07 22:00:14

70

Views

Calculating Colimits in The category of Simplicial Sets

Published on 07 Jul 2022 - 22:00

score 417 · Answer 8 · 2022-07-08 17:02:59

417

Views

Is taking (co)limits exact in an Abelian category?

Published on 08 Jul 2022 - 17:02

score 34 · Answer 9 · 2022-07-12 20:39:26

34

Views

"Lifting" of (generalized) elements of colimits along maps of diagrams

Published on 12 Jul 2022 - 20:39

score 132 · Answer 10 · 2022-08-07 19:22:15

132

Views

Inverse limit of compact hausdorff spaces

Published on 07 Aug 2022 - 19:22

score 25 · Answer 11 · 2026-03-28 08:50:09

25

Views

Field of formal Laurent series as a colimit of fractions

Published on 28 Mar 2026 - 8:50

score 118 · Answer 12 · 2022-08-09 21:07:04

118

Views

When is $f$ not the coequalizer of its kernel pair?

Published on 09 Aug 2022 - 21:07

score 53 · Answer 13 · 2022-08-13 12:14:50

53

Views

Showing the Krull topology is the same as the categorical limit topology of (infinite) Galois extensions - is my solution correct?

Published on 13 Aug 2022 - 12:14

score 44 · Answer 14 · 2022-08-18 02:50:42

44

Views

Direct limit of sequences induced by fusing together copies of $\mathbb{Z}$

Published on 18 Aug 2022 - 2:50

score 360 · Answer 15 · 2026-03-27 06:12:35

360

Views

Is the inverse limit of quotient the quotient of inverse limits?

Published on 27 Mar 2026 - 6:12

List Question

Given a sub-presheaf $(F,\alpha)\subseteq X$, how does one create subobjects $y_{A,x}\subseteq\scr{A}$ $(\cdot,A)$ for all $(A,x)\in\int_\scr{A}$ $X$?

To prove $ \Bbb{Z}_p$ is isomorphic to $\lim_{←}\Bbb{Z}_p/p^n \Bbb{Z}_p$ as a ring

Is there a simple abstract reason why a profinite group is an inverse limit of finite groups?

Symmetry of colimits

How necessary is the filteredness condition in the result “a filtered diagram in which all morphisms are isomorphisms has a colimit”?

Definition of Limits in Category Theory

Calculating Colimits in The category of Simplicial Sets

Is taking (co)limits exact in an Abelian category?

"Lifting" of (generalized) elements of colimits along maps of diagrams

Inverse limit of compact hausdorff spaces

Field of formal Laurent series as a colimit of fractions

When is $f$ not the coequalizer of its kernel pair?

Showing the Krull topology is the same as the categorical limit topology of (infinite) Galois extensions - is my solution correct?

Direct limit of sequences induced by fusing together copies of $\mathbb{Z}$

Is the inverse limit of quotient the quotient of inverse limits?

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