Not signed in (Sign In)

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 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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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 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

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.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2011
    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeDec 7th 2011

    There’s no reason to restrict this definition to the cartesian case, is there? It seems to make sense for any closed (symmetric?) monoidal category — or maybe even any closed category.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2011
    • (edited Dec 7th 2011)

    Sure, but creating this entry was motivated from figuring out how precisely the term “strong” here is used in “classical” literature. Of course we can point that out in the entry and still generalize it.

    Also the variant [f !X,Y]f *[X,f *Y][f_! X, Y] \simeq f_* [X, f^* Y] deserves be called “strong adjunction”, it seems.

    I am agnostic about this. All I want eventually is to avoid that people interrupt my talks saying that I use “strong” in a bad way. :-)

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeDec 8th 2011

    I’ve seen “strong” used in something like this way in the monoidal case as well. For instance we have strong functors and monads.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 8th 2011

    All I want eventually is to avoid that people interrupt my talks saying that I use “strong” in a bad way. :-)

    Yes, because there seems to be nothing categorists like more than a long, drawn-out terminological debate! Witness the discussion on the categories list on schizophrenic objects (again!).

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 8th 2011

    I know what you mean. But I should mention that the person who wondered about my use of “strong” did so in a very sensible and helpful way. And I agree that my use of the word was not optimal, and that I need to think about changing something.

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeDec 8th 2011
    • (edited Dec 8th 2011)

    Luc Illusie said somewhere that when he would submit a manuscript to his advisor, certain guy with the name Alexander Grothendieck, that the manuscript was returned full of red marks, at all levels, from the factual corrections, improvements of the proof, additional requests to the linguistic, stylistic remarks and even orthography and commas…He enjoyed that, but the new list of red marks reappeared after a thorough revision. At the end he ignored repeating a process after 2nd iteration or so, wanting to finish a process.

    It is always enjoyable to get suggestions for improvements unless they are too stiff requests to substantially slow down (or even stop) the creation or publishing process. I had once a referee who rejected the paper with only a long list of stylistic corrections and no single content disagreement (well one, but in which the referee was trivially wrong, by the textbook fact). A problem with discussions in publishing process is that the editor or the referee can simply ignore you and just act by decision and power of the will; in the current way the things work, they are not obligated to listen for a scientific argument, plus they can (somewhat justified, but not always) hide behind the vague value statements like “important”, “difficult” and alike. With current publication pressure in which too many try to publish prematurely, the editors have just more reasons, not to attend the details and ignore even on the level of superficial negative feeling.

    • CommentRowNumber8.
    • CommentAuthormaxsnew
    • CommentTimeJan 19th 2024

    Am I correct that this is the same as an enriched adjunction where we view the CCC as self-enriched?