Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
  
  
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorJohn Baez
   • CommentTimeSep 29th 2024
   • PermaLink
   Author: John Baez
   Format: MarkdownItexI think the second sentence below needs to have the phrase "torsion-free" added to it twice. Right? I'm going to do that. > a) The category $\lambda Ring$ of $\lambda$-rings is [[monadic]] and [[comonadic]] over the category of $C Ring$ of commutative rings. > b) The category $\lambda Ring_{\neg tor}$ of $\lambda$-rings is [[monadic]] and [[comonadic]] over the category of $C Ring_{\neg tor}$ of commutative rings. <a href="https://ncatlab.org/nlab/revision/diff/Lambda-ring/46">diff</a>, <a href="https://ncatlab.org/nlab/revision/Lambda-ring/46">v46</a>, <a href="https://ncatlab.org/nlab/show/Lambda-ring">current</a>

   I think the second sentence below needs to have the phrase “torsion-free” added to it twice. Right? I’m going to do that.

   a) The category of -rings is monadic and comonadic over the category of of commutative rings.

   b) The category of -rings is monadic and comonadic over the category of of commutative rings.

   diff, v46, current