Question

Let $t: I \to \mathcal C$ be a funtor with $I$ small, and suppose that $t$ has a colimit. Prove that $\lim_{\to} (F \circ t)$ exists

score 38 · Answer 1 · 2026-05-10 15:52:32

38

Views

Let $t: I \to \mathcal C$ be a funtor with $I$ small, and suppose that $t$ has a colimit. Prove that $\lim_{\to} (F \circ t)$ exists

Published on 10 May 2026 - 15:52

score 630 · Answer 2 · 2026-05-10 18:03:28

630

Views

Show that $\lim$ is a right adjoint to the constant functor

Published on 10 May 2026 - 18:03

score 48 · Answer 3 · 2026-04-16 04:02:13

Limit of $h_{\mathcal C} \circ F$ for $F: I \to \mathcal C$ exists in $\text{Func}(\mathcal C^\text{op}, \text{Set)}$ and is $\text{Hom}(\_,\lim F)$.

score 386 · Answer 4 · 2026-04-10 16:25:29

386

Views

Simple example of product not preserving coequaliser in $\mathbf{Top}$

Published on 10 Apr 2026 - 16:25

score 141 · Answer 5 · 2026-04-11 22:49:58

141

Views

Colimits where maps in are determined by maps into a component?

Published on 11 Apr 2026 - 22:49

score 244 · Answer 6 · 2026-04-11 16:52:46

244

Views

Direct limit of functions

Published on 11 Apr 2026 - 16:52

score 195 · Answer 7 · 2026-05-10 17:55:57

195

Views

Coends and adjunctions

Published on 10 May 2026 - 17:55

score 573 · Answer 8 · 2026-04-14 19:07:31

573

Views

Sheaf on basic open sets.

Published on 14 Apr 2026 - 19:07

score 116 · Answer 9 · 2026-04-14 14:49:16

116

Views

Colimit of discrete diagram (coproduct) is the tensor product

Published on 14 Apr 2026 - 14:49

score 75 · Answer 10 · 2026-04-14 01:58:24

75

Views

Not-quite-preservation of not-quite-filtered colimits

Published on 14 Apr 2026 - 1:58

score 64 · Answer 11 · 2026-05-10 14:53:38

64

Views

VAR, Algebra and local presentability

Published on 10 May 2026 - 14:53

score 193 · Answer 12 · 2026-04-12 19:45:26

193

Views

Why do we need isomorphism between a diagram and a cone L for it to be a limit?

Published on 12 Apr 2026 - 19:45

score 49 · Answer 13 · 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 72 · Answer 14 · 2026-04-09 07:49:48

72

Views

Open set in a product of colimits

Published on 09 Apr 2026 - 7:49

score 1.1k · Answer 15 · 2026-04-12 16:53:02

1.1k

Views

Filtered colimits commute with finite limits

Published on 12 Apr 2026 - 16:53

List Question

Let $t: I \to \mathcal C$ be a funtor with $I$ small, and suppose that $t$ has a colimit. Prove that $\lim_{\to} (F \circ t)$ exists

Show that $\lim$ is a right adjoint to the constant functor

Limit of $h_{\mathcal C} \circ F$ for $F: I \to \mathcal C$ exists in $\text{Func}(\mathcal C^\text{op}, \text{Set)}$ and is $\text{Hom}(\_,\lim F)$.

Simple example of product not preserving coequaliser in $\mathbf{Top}$

Colimits where maps in are determined by maps into a component?

Direct limit of functions

Coends and adjunctions

Sheaf on basic open sets.

Colimit of discrete diagram (coproduct) is the tensor product

Not-quite-preservation of not-quite-filtered colimits

VAR, Algebra and local presentability

Why do we need isomorphism between a diagram and a cone L for it to be a limit?

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

Open set in a product of colimits

Filtered colimits commute with finite limits

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