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 34 · Answer 1 · 2018-10-21 20:10:15

34

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 21 Oct 2018 - 20:10

score 624 · Answer 2 · 2018-10-21 22:19:07

624

Views

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

Published on 21 Oct 2018 - 22:19

score 45 · Answer 3 · 2018-10-22 00:41:56

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 383 · Answer 4 · 2018-10-24 16:19:16

383

Views

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

Published on 24 Oct 2018 - 16:19

score 138 · Answer 5 · 2018-10-26 07:24:48

138

Views

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

Published on 26 Oct 2018 - 7:24

score 240 · Answer 6 · 2018-10-26 16:08:29

240

Views

Direct limit of functions

Published on 26 Oct 2018 - 16:08

score 190 · Answer 7 · 2018-11-02 12:31:48

190

Views

Coends and adjunctions

Published on 02 Nov 2018 - 12:31

score 569 · Answer 8 · 2018-11-03 13:26:36

569

Views

Sheaf on basic open sets.

Published on 03 Nov 2018 - 13:26

score 113 · Answer 9 · 2018-11-03 23:51:25

113

Views

Colimit of discrete diagram (coproduct) is the tensor product

Published on 03 Nov 2018 - 23:51

score 72 · Answer 10 · 2018-11-04 12:56:48

72

Views

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

Published on 04 Nov 2018 - 12:56

score 58 · Answer 11 · 2018-11-13 20:03:57

58

Views

VAR, Algebra and local presentability

Published on 13 Nov 2018 - 20:03

score 191 · Answer 12 · 2018-11-18 20:28:50

191

Views

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

Published on 18 Nov 2018 - 20:28

score 43 · Answer 13 · 2026-03-16 22:29:57

43

Views

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

Published on 16 Mar 2026 - 22:29

score 68 · Answer 14 · 2018-11-25 21:05:46

68

Views

Open set in a product of colimits

Published on 25 Nov 2018 - 21:05

score 1.1k · Answer 15 · 2018-11-28 17:09:12

1.1k

Views

Filtered colimits commute with finite limits

Published on 28 Nov 2018 - 17:09

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

Trending Questions

Popular # Hahtags

Popular Questions