Question

Equivalence of categories preserves cartesian closedness

score 191 · Answer 1 · 2020-02-05 18:41:59

191

Views

Equivalence of categories preserves cartesian closedness

Published on 05 Feb 2020 - 18:41

score 258 · Answer 2 · 2020-02-06 22:53:49

258

Views

Internal Union Arrows In A Topos

Published on 06 Feb 2020 - 22:53

score 129 · Answer 3 · 2026-03-25 22:02:52

129

Views

Exponents in $\mathbf{Sets}^{G^{{\rm op}}}$ for an arbitrary group $G$.

Published on 25 Mar 2026 - 22:02

score 240 · Answer 4 · 2026-03-27 07:17:02

240

Views

Show a $G$-set $(X,\mu: X\times G\to X)$ has continuous $\mu$ iff for each $x\in X$ its isotropy group is open.

Published on 27 Mar 2026 - 7:17

score 206 · Answer 5 · 2026-03-26 14:29:00

206

Views

Dedekind-infinite objects and NNO in an elementary topos

Published on 26 Mar 2026 - 14:29

score 183 · Answer 6 · 2026-03-25 22:10:57

183

Views

Exercise I.6(b) of "Sheaves in Geometry and Logic [. . .]".

Published on 25 Mar 2026 - 22:10

score 60 · Answer 7 · 2026-03-25 22:03:14

60

Views

Conclude that $\mathbf{B}G$ is a CCC using previous questions in "Sheaves in Geometry and Logic [. . .]".

Published on 25 Mar 2026 - 22:03

score 80 · Answer 8 · 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 121 · Answer 9 · 2020-02-14 06:01:14

121

Views

Subobject of a product

Published on 14 Feb 2020 - 6:01

score 170 · Answer 10 · 2020-02-14 06:03:56

170

Views

Axioms of a Local Set Theory

Published on 14 Feb 2020 - 6:03

score 200 · Answer 11 · 2026-02-23 03:27:10

200

Views

The forgetful functor $U:\mathbf{B}G\to\mathbf{Sets}$ need not preserve infinite limits.

Published on 23 Feb 2026 - 3:27

score 98 · Answer 12 · 2026-03-27 23:39:30

98

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 27 Mar 2026 - 23:39

score 191 · Answer 13 · 2026-03-25 22:30:56

191

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 25 Mar 2026 - 22:30

score 38 · Answer 14 · 2020-02-16 10:11:38

38

Views

$Et/X$ is closed under finite limits in $Top/X$.

Published on 16 Feb 2020 - 10:11

score 126 · Answer 15 · 2026-03-25 22:25:56

126

Views

Proving Proposition I.5.1 of Mac Lane and Moerdijk.

Published on 25 Mar 2026 - 22:25

List Question

Equivalence of categories preserves cartesian closedness

Internal Union Arrows In A Topos

Exponents in $\mathbf{Sets}^{G^{{\rm op}}}$ for an arbitrary group $G$.

Show a $G$-set $(X,\mu: X\times G\to X)$ has continuous $\mu$ iff for each $x\in X$ its isotropy group is open.

Dedekind-infinite objects and NNO in an elementary topos

Exercise I.6(b) of "Sheaves in Geometry and Logic [. . .]".

Conclude that $\mathbf{B}G$ is a CCC using previous questions in "Sheaves in Geometry and Logic [. . .]".

How does the functor Sub act on representable Presheaves?

Subobject of a product

Axioms of a Local Set Theory

The forgetful functor $U:\mathbf{B}G\to\mathbf{Sets}$ need not preserve infinite 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 $\Omega(q)=\{r\mid r\in\mathbf{R^+},r\ge q\}.$

$Et/X$ is closed under finite limits in $Top/X$.

Proving Proposition I.5.1 of Mac Lane and Moerdijk.

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