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: algebraic category

Bottom of Page

1 to 6 of 6

  1.  
    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 1st 2020

    Added a reference to Adámek-Rosický-Vitale.

    diff, v12, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 1st 2020
    • (edited Dec 1st 2020)

    The book by Adámek–Rosický–Vitale uses a different definition of an algebraic category: an algebraic category is a category equivalent to the category of algebras over an algebraic theory, i.e., the category of functors T→Set that preserve finite products, where T is a small category with finite products.

    This definition seems to be much more widely used these days than the older definition of Adámek–Herrlich–Strecker.

    Should we adjust the article accordingly? Is the older definition of Adámek–Herrlich–Strecker actually used anywhere other than in their book?

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 13th 2020

    Added the original paper by Lawvere.

    diff, v13, current

    • CommentRowNumber4.
    • CommentAuthorGuest
    • CommentTimeJan 25th 2022
    When is an abelian category algebraic?
    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeMar 17th 2023

    I wonder if it is possible to generalize from algebraic categories to algebraic (infinity,1)-categories and thus whether it is possible to talk about trivial algebras in algebraic (infinity,1)-categories, such as trivial H-spaces and trivial A-infinity spaces.

  6. Linked new page for Field, the category of fields.

    diff, v16, current

1 to 6 of 6

  1.