Not signed in (Sign In)

Start a new discussion

Not signed in

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

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory 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 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 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 sheaves simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorvarkor
    • CommentTimeSep 7th 2021

    Added link to internal hom.

    diff, v3, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 8th 2021

    Thanks for the alert. I wasn’t aware of this entry from 2017.

    It seems strange to have this classical concept discussed here in a duplicate entry under a non-clasical name with a single and non-classical reference. I wonder what the original rationale was.

    Anyway, this entry should be merged with internal hom.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 8th 2021

    I have added at least a remark line at the very top of the entry, and another one above its single reference, clarifying that this entry is (unless I am missing something) a partial duplicate of internal hom.

    If anyone knows what the story is with “residual” and whether there is a reason to keep this as a separate entry, please let us know.

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 8th 2021

    It’s something that gets used in eg semantic models for substructural logics, which is where than Melliès–Zeilberger paper is coming from. But I agree that it shouldn’t need its own page, but a redirect and a terminology discussion at eg internal hom

    • CommentRowNumber5.
    • CommentAuthorTim_Porter
    • CommentTimeSep 8th 2021
    • (edited Sep 8th 2021)

    There is mention of residuated lattice in relation to ideals in monoids. The link is grey, so I will create a stub entry on this. There could be perhaps additions on solving equations over idempotent semirings. I will see what I can dig up. The relations with algebras of relations, etc., may be worth chasing up with ideas about the categorification.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeSep 8th 2021

    Thanks. If “residual” is an established term that substructural logic readers would appreciate to be reading up on, then having an entry on it makes perfect sense. But then the present entry needs to be rewritten, as currently it gives no idea that this is the case.

    • CommentRowNumber7.
    • CommentAuthorTim_Porter
    • CommentTimeSep 9th 2021

    Added a phrase to hint that there are other meanings.

    diff, v6, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)