Question

The forgetful functor $U: \text{Con}(\mathcal C) \to \mathcal C$ has a left adjoint.

score 119 · Answer 1 · 2026-02-23 05:10:58

119

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The forgetful functor $U: \text{Con}(\mathcal C) \to \mathcal C$ has a left adjoint.

Published on 23 Feb 2026 - 5:10

score 46 · Answer 2 · 2021-01-15 20:15:31

46

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The unit $\eta$ of an adjunction satisfies $\sigma \circ \eta = 1$ if and only if $\Gamma_{C, C'} \circ \mathbb F_{C, C'} = 1$.

Published on 15 Jan 2021 - 20:15

score 88 · Answer 3 · 2021-01-18 17:01:01

88

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Does the internal category forgetful functor have both adjoints?

Published on 18 Jan 2021 - 17:01

score 114 · Answer 4 · 2021-01-21 19:03:55

$\Gamma: \mathcal C \to \text{Fun}(\mathcal Z, \mathcal C)$ has a left adjoint iff all $F \in \text{Fun}(\mathcal Z, \mathcal C)$ has a colimit.

score 84 · Answer 5 · 2021-01-22 16:41:18

84

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Does the 'arrow' internal category forgetful functor have a right adjoint?

Published on 22 Jan 2021 - 16:41

score 44 · Answer 6 · 2021-02-05 15:56:53

44

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Does the 'arrow' internal category functor preserve binary coproducts?

Published on 05 Feb 2021 - 15:56

score 287 · Answer 7 · 2026-03-25 09:31:47

287

Views

Right adjoint of pullback functor

Published on 25 Mar 2026 - 9:31

score 218 · Answer 8 · 2026-03-26 06:33:55

218

Views

How can I compute a monad from this adjunction?

Published on 26 Mar 2026 - 6:33

score 157 · Answer 9 · 2026-02-23 02:57:44

157

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How to understand the Grothendieck group as an adjoint?

Published on 23 Feb 2026 - 2:57

score 211 · Answer 10 · 2021-02-22 12:30:45

211

Views

Examples of functors which have both adjoints

Published on 22 Feb 2021 - 12:30

score 139 · Answer 11 · 2021-02-24 10:59:06

139

Views

Adjoint Functors Operating On Natural Transformations

Published on 24 Feb 2021 - 10:59

score 234 · Answer 12 · 2026-02-23 05:17:47

234

Views

Forgetful functor from Magma to Set

Published on 23 Feb 2026 - 5:17

score 304 · Answer 13 · 2021-03-03 05:26:33

304

Views

If a forgetful functor between varieties preserves coproducts, does it have a right adjoint?

Published on 03 Mar 2021 - 5:26

score 85 · Answer 14 · 2026-03-27 23:01:11

85

Views

adjunctions from either the category of small categories or the category of groupoids

Published on 27 Mar 2026 - 23:01

score 86 · Answer 15 · 2021-03-04 09:08:06

86

Views

Sums factor as products in internal hom functor

Published on 04 Mar 2021 - 9:08

List Question

The forgetful functor $U: \text{Con}(\mathcal C) \to \mathcal C$ has a left adjoint.

The unit $\eta$ of an adjunction satisfies $\sigma \circ \eta = 1$ if and only if $\Gamma_{C, C'} \circ \mathbb F_{C, C'} = 1$.

Does the internal category forgetful functor have both adjoints?

$\Gamma: \mathcal C \to \text{Fun}(\mathcal Z, \mathcal C)$ has a left adjoint iff all $F \in \text{Fun}(\mathcal Z, \mathcal C)$ has a colimit.

Does the 'arrow' internal category forgetful functor have a right adjoint?

Does the 'arrow' internal category functor preserve binary coproducts?

Right adjoint of pullback functor

How can I compute a monad from this adjunction?

How to understand the Grothendieck group as an adjoint?

Examples of functors which have both adjoints

Adjoint Functors Operating On Natural Transformations

Forgetful functor from Magma to Set

If a forgetful functor between varieties preserves coproducts, does it have a right adjoint?

adjunctions from either the category of small categories or the category of groupoids

Sums factor as products in internal hom functor

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