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To prove the Nullstellensatz, how can the general case of an arbitrary algebraically closed field be reduced to the easily-proved case of an uncountable algebraically closed field?

ac.commutative-algebra

jan 6 at 18:08 Martin Brandenburg 29.1k●2●45●129

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675

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What is the motivation for maps of adjunctions?

ct.category-theory

may 29 10 at 12:54 Buschi Sergio 1,799●1●3●8

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690

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If F is left adjoint to G, when does FG preserve limits? When do counits interchange with limits?

ct.category-theory

jul 13 10 at 20:22 MathOverflow♦ 1●2●3

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367

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What are the ‘standard’ applications of the duals of the adjoint functor theorems?

ct.category-theory

mar 8 10 at 2:20 Mike Shulman 17.2k●20●70

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298

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What is a reference for an explicit, logic-based, statement of duality in category theory (in ‘'complicated’' situations)? And what are the prerequisites for a beginner in logic?

ct.category-theory lo.logic reference-request

apr 5 10 at 0:57 Reid Barton 14.4k●1●28●85

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358

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Why is Top_4 a reflective subcategory of Top_3?

ct.category-theory gn.general-topology

dec 22 09 at 3:58 Greg Kuperberg 36.2k●2●116●179

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335

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If G is monadic and the comparison functor is an equivalence that is not an isomorphism, does G create limits?

ct.category-theory

may 13 10 at 2:37 Todd Trimble 22.3k●1●62●96

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Questions

To prove the Nullstellensatz, how can the general case of an arbitrary algebraically closed field be reduced to the easily-proved case of an uncountable algebraically closed field?

What is the motivation for maps of adjunctions?

If F is left adjoint to G, when does FG preserve limits? When do counits interchange with limits?

What are the ‘standard’ applications of the duals of the adjoint functor theorems?

What is a reference for an explicit, logic-based, statement of duality in category theory (in ‘'complicated’' situations)? And what are the prerequisites for a beginner in logic?

Why is Top_4 a reflective subcategory of Top_3?

If G is monadic and the comparison functor is an equivalence that is not an isomorphism, does G create limits?

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