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).

nLab > Latest Changes: homological category

Bottom of Page

1 to 8 of 8

  1.  
    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeMay 23rd 2011
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 23rd 2011

    Probably in the first line you meant to write “homological” instead of “regular”.

    • CommentRowNumber3.
    • CommentAuthorjim_stasheff
    • CommentTimeMay 24th 2011
    It would help to have a brief summary of what makes a cat homological!
    I assume it is NOT just a dg cat?
    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeMay 24th 2011

    Of course it is not. It is not an enriched category, but an ordinary one category satisfying some conditions. Of course, the homological algebra is then done with an appropriate notion of complexes in it and the five lemma is a lemma in the original category. Typical examples are categories of algebras over certain subclass of algebraic theories in Set. Every semi-abelian category is an example. There is also a generalization, relative homological categories.

    Jim, I and mislead and do not like the terminology in this case either. It is misleading. Bourn and Janelidze thank Johnstone for the help with terminology, and my experience in past is that Johnstone often has strange inventions in terminology.

    • CommentRowNumber5.
    • CommentAuthorTim_Porter
    • CommentTimeDec 9th 2018

    Fixed some formatting

    diff, v7, current

  6. Added sidebar, TOC, section headings, related entries, and more details to a reference.

    Rongmin Lu

    diff, v8, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 22nd 2021

    I have added (here) the example of GrpGrp, with pointers to why this is homological (a fact that the references listed here forget to make explicit)

    diff, v10, current

    • CommentRowNumber8.
    • CommentAuthorAli Caglayan
    • CommentTimeJan 14th 2024
    • (edited Jan 14th 2024)
    Edit: Nevermind, I was mistaken.

1 to 8 of 8

  1.