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 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 sheaves 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
    • CommentTimeMar 9th 2011
    • (edited Mar 9th 2011)

    once I typed out at category of monoids some details of the tedious construction of pushouts in Monoids(C)Monoids(C) (for CC a symmetric monoidal category) along a morphism of free monoids

    F(K) A F(v) F(L) A F(K)F(L) \array{ F(K) &\to& A \\ {}^{\mathllap{F(v)}}\downarrow && \downarrow \\ F(L) &\to& A \coprod_{F(K)} F(L) }

    for some morphism v:KLv : K \to L in the underlying category CC.

    I remember when typing this I thought I knew how this simplifies in the case of commutative monoids. But now I come back to this, find that I forgot what I knew and need to think again.

    Is in CommMonoids(C)CommMonoids(C) the pushout of the above kind given by the pushout in the underlying category CC?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 9th 2011

    oh, I am being stupid. For instance page 478 of the Elephant has what I need. I’ll write out something into the nnLab, lest I forget again.