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.
   • CommentAuthorDmitri Pavlov
   • CommentTimeOct 19th 2015
   • (edited Oct 20th 2015)
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexSuppose P is a (colored) [[prop]] in a closed symmetric monoidal locally presentable category C. Is the category Alg_P of algebras over P in C locally presentable? It seems that one can relatively easy establish the accessibility of algebras over P using [[PIE-limits]]. However, the forgetful functor Alg_P→C preserves neither limits nor colimits, so it's unclear how one could establish the (co)completeness of Alg_P (is this even true?).

   Suppose P is a (colored) prop in a closed symmetric monoidal locally presentable category C. Is the category Alg_P of algebras over P in C locally presentable?

   It seems that one can relatively easy establish the accessibility of algebras over P using PIE-limits.

   However, the forgetful functor Alg_P→C preserves neither limits nor colimits, so it’s unclear how one could establish the (co)completeness of Alg_P (is this even true?).

2. • CommentRowNumber2.
   • CommentAuthorDmitri Pavlov
   • CommentTimeOct 20th 2015
   • (edited Oct 20th 2015)
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexNow on MathOverflow: <http://mathoverflow.net/questions/221403/when-are-the-categories-of-algebras-over-props-cocomplete>

   Now on MathOverflow: http://mathoverflow.net/questions/221403/when-are-the-categories-of-algebras-over-props-cocomplete