Question

Prove that $\mathbf{FinSets}^{\mathbf{N}}$ has no subobject classifier.

score 309 · Answer 1 · 2020-02-01 23:43:39

309

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Prove that $\mathbf{FinSets}^{\mathbf{N}}$ has no subobject classifier.

Published on 01 Feb 2020 - 23:43

score 166 · Answer 2 · 2020-02-04 10:16:37

166

Views

Understanding contravariant functors and inner products

Published on 04 Feb 2020 - 10:16

score 80 · Answer 3 · 2026-02-23 08:21:46

80

Views

How does the functor Sub act on representable Presheaves?

Published on 23 Feb 2026 - 8:21

score 207 · Answer 4 · 2020-02-14 02:37:25

207

Views

Forgetful functors from categories of algebra create limits?

Published on 14 Feb 2020 - 2:37

score 96 · Answer 5 · 2026-03-25 13:54:47

96

Views

Show that $T^S$ with an evaluation is indeed the exponential in the functor category $\hat{\mathbf{C}}=\mathbf{Sets}^{\mathbf{C}^{{\rm op}}}.$

Published on 25 Mar 2026 - 13:54

score 190 · Answer 6 · 2020-02-15 17:28:13

190

Views

In $\mathbf{Sets}^\mathbf{Q}$, prove the subobject classifier $\Omega$ is given by $\Omega(q)=\{r\mid r\in\mathbf{R^+},r\ge q\}.$

Published on 15 Feb 2020 - 17:28

score 125 · Answer 7 · 2020-02-16 20:07:13

125

Views

Proving Proposition I.5.1 of Mac Lane and Moerdijk.

Published on 16 Feb 2020 - 20:07

score 37 · Answer 8 · 2026-03-24 17:17:46

37

Views

Is defining sampling as a functor from the category of stochastic relations to a sub category of sets valid?

Published on 24 Mar 2026 - 17:17

score 293 · Answer 9 · 2026-03-25 04:32:45

293

Views

A sieve $S$ on $U$ in the category $\mathcal{O}(X)$ is principal iff the corresponding subfunctor $S\subset 1_U\cong{\rm Hom}(-,U)$ is a sheaf.

Published on 25 Mar 2026 - 4:32

score 95 · Answer 10 · 2020-02-28 02:43:02

95

Views

What is the name of this identity relating the monoidal products of finite sets and finite-dimensional vector spaces?

Published on 28 Feb 2020 - 2:43

score 97 · Answer 11 · 2026-03-24 09:13:25

97

Views

Introductory exercise of category theory

Published on 24 Mar 2026 - 9:13

score 95 · Answer 12 · 2020-02-28 22:26:23

95

Views

. . . and what about $\Gamma$ in $\S II.5$ of Mac Lane and Moerdijk?

Published on 28 Feb 2020 - 22:26

score 326 · Answer 13 · 2020-02-29 18:13:21

326

Views

Show that $\Gamma$, $\Lambda$, and the associated sheaf functor are all left exact.

Published on 29 Feb 2020 - 18:13

score 84 · Answer 14 · 2026-03-21 12:48:03

84

Views

Showing that $H_A\simeq H_{A'}$ implies $A\simeq A'$

Published on 21 Mar 2026 - 12:48

score 134 · Answer 15 · 2020-03-01 10:05:12

134

Views

Can functoriality be explained in the opposite way?

Published on 01 Mar 2020 - 10:05

List Question

Prove that $\mathbf{FinSets}^{\mathbf{N}}$ has no subobject classifier.

Understanding contravariant functors and inner products

How does the functor Sub act on representable Presheaves?

Forgetful functors from categories of algebra create limits?

Show that $T^S$ with an evaluation is indeed the exponential in the functor category $\hat{\mathbf{C}}=\mathbf{Sets}^{\mathbf{C}^{{\rm op}}}.$

In $\mathbf{Sets}^\mathbf{Q}$, prove the subobject classifier $\Omega$ is given by $\Omega(q)=\{r\mid r\in\mathbf{R^+},r\ge q\}.$

Proving Proposition I.5.1 of Mac Lane and Moerdijk.

Is defining sampling as a functor from the category of stochastic relations to a sub category of sets valid?

A sieve $S$ on $U$ in the category $\mathcal{O}(X)$ is principal iff the corresponding subfunctor $S\subset 1_U\cong{\rm Hom}(-,U)$ is a sheaf.

What is the name of this identity relating the monoidal products of finite sets and finite-dimensional vector spaces?

Introductory exercise of category theory

. . . and what about $\Gamma$ in $\S II.5$ of Mac Lane and Moerdijk?

Show that $\Gamma$, $\Lambda$, and the associated sheaf functor are all left exact.

Showing that $H_A\simeq H_{A'}$ implies $A\simeq A'$

Can functoriality be explained in the opposite way?

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