Question

Representability $h_C(X) \simeq F$ of functors determines rep. $X$ up to unique isomorphism (using Yoneda Lemma).

score 548 · Answer 1 · 2026-03-25 03:21:22

548

Views

Representability $h_C(X) \simeq F$ of functors determines rep. $X$ up to unique isomorphism (using Yoneda Lemma).

Published on 25 Mar 2026 - 3:21

score 445 · Answer 2 · 2026-03-27 04:19:30

445

Views

In a category is the direct limit an exact functor?

Published on 27 Mar 2026 - 4:19

score 52 · Answer 3 · 2026-03-25 17:41:57

52

Views

"Cats & Sheaves" defines $C_A$ w.r.t $F : C \to C'$ for object $A \in C'$, but then doesn't define $C_F$...

Published on 25 Mar 2026 - 17:41

score 403 · Answer 4 · 2017-08-23 17:37:39

403

Views

The first non-trivial Schur functor

Published on 23 Aug 2017 - 17:37

score 162 · Answer 5 · 2017-08-24 02:01:39

162

Views

Computing $\mathrm{Tor}_{i}^{R}(M,(x^k))$, where $R=\mathbb{Z}[x]/(x^n)$

Published on 24 Aug 2017 - 2:01

score 346 · Answer 6 · 2017-08-25 10:52:57

346

Views

Faithful implies left-invertible functor, counterexample

Published on 25 Aug 2017 - 10:52

score 95 · Answer 7 · 2026-03-25 19:04:24

95

Views

The isomorphism $F \simeq h_C(X)$ determines $X$ how?

Published on 25 Mar 2026 - 19:04

score 320 · Answer 8 · 2017-08-28 13:45:40

320

Views

If $F : Ab \rightarrow Ab$ is an additive functor and $0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0$ is an exact split sequence then ...

Published on 28 Aug 2017 - 13:45

score 68 · Answer 9 · 2026-03-27 00:34:58

Let $F: Ab \rightarrow Ab$ be an additive functor and $I$ a finite index set, show that $F(\sum_{i \in I} A_i) \approx \sum_{i \in I} F(A_i)$

score 513 · Answer 10 · 2017-08-29 10:39:14

513

Views

Is this functor full? Top^op -> CRing (ring of real-valued continuous functions on a topological space)

Published on 29 Aug 2017 - 10:39

score 180 · Answer 11 · 2017-08-29 11:10:42

180

Views

For natural transformation $\eta$ and functor $L$, is $(\eta \circ L)_X \equiv \eta_{L(X)}$ by definition?

Published on 29 Aug 2017 - 11:10

score 38 · Answer 12 · 2017-08-30 13:47:35

38

Views

How can this be a complex if each term isn't an abelian group?

Published on 30 Aug 2017 - 13:47

score 123 · Answer 13 · 2017-08-30 15:11:54

123

Views

How would I use induction to prove that this map exists?

Published on 30 Aug 2017 - 15:11

score 362 · Answer 14 · 2026-03-25 18:25:44

362

Views

Question on slice category

Published on 25 Mar 2026 - 18:25

score 203 · Answer 15 · 2017-09-19 18:30:23

203

Views

If $F$ and $G$ are biadjoint, how is $\operatorname{Nat}(F,F)\simeq\operatorname{Nat}(G\circ F,1)$?

Published on 19 Sep 2017 - 18:30

List Question

Representability $h_C(X) \simeq F$ of functors determines rep. $X$ up to unique isomorphism (using Yoneda Lemma).

In a category is the direct limit an exact functor?

"Cats & Sheaves" defines $C_A$ w.r.t $F : C \to C'$ for object $A \in C'$, but then doesn't define $C_F$...

The first non-trivial Schur functor

Computing $\mathrm{Tor}_{i}^{R}(M,(x^k))$, where $R=\mathbb{Z}[x]/(x^n)$

Faithful implies left-invertible functor, counterexample

The isomorphism $F \simeq h_C(X)$ determines $X$ how?

If $F : Ab \rightarrow Ab$ is an additive functor and $0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0$ is an exact split sequence then ...

Let $F: Ab \rightarrow Ab$ be an additive functor and $I$ a finite index set, show that $F(\sum_{i \in I} A_i) \approx \sum_{i \in I} F(A_i)$

Is this functor full? Top^op -> CRing (ring of real-valued continuous functions on a topological space)

For natural transformation $\eta$ and functor $L$, is $(\eta \circ L)_X \equiv \eta_{L(X)}$ by definition?

How can this be a complex if each term isn't an abelian group?

How would I use induction to prove that this map exists?

Question on slice category

If $F$ and $G$ are biadjoint, how is $\operatorname{Nat}(F,F)\simeq\operatorname{Nat}(G\circ F,1)$?

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