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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

feb 25 at 12:55 Emerton 15.7k●36●80

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390

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What is the motivation for maps of adjunctions?

ct.category-theory

may 29 at 12:54 Buschi Sergio 117●2

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601

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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 at 20:22 MathOverflow♦ 1●1●3

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245

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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 at 0:57 Reid Barton 12.1k●1●19●71

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

ct.category-theory

mar 8 at 2:20 Mike Shulman 5,218●3●21

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265

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Why is Top_4 a reflective subcategory of Top_3?

ct.category-theory gn.general-topology

dec 22 at 3:58 Greg Kuperberg 18.6k●1●43●94

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142

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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 at 2:37 Todd Trimble 1,208●2●10

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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 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?

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

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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