A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
On generalizing free algebras for a functor

2012
*
Journal of Logic and Computation
*

In this paper we introduce

doi:10.1093/logcom/exs016
fatcat:rvo2naz4pjd43g5ujid4gobjay
*a*new setting, based*on*partial*algebras*,*for*studying constructions of finitely*generated**free**algebras*. ... In particular, our method encompasses the construction of finitely*generated**free**algebras**for*varieties of*algebras**for**a**functor*as in [2], Heyting*algebras*as in [1] and S4*algebras*as in [8] . ... We give*a*sufficient condition*for*the*free*image-total*functor**for**a*logic to yield the*free*total*algebra*in the colimit. • Section 4. ...##
###
Birings and plethories of integer-valued polynomials

2010
*
Actes des rencontres du CIRM
*

This holds in particular if θn is an isomorphism

doi:10.5802/acirm.34
fatcat:snet665v7je7rkk36mq56t6vla
*for*all n, which in turn holds,*for*example, if D is*a*Krull domain or more*generally**a*TV PVMD. ... Let*A*and B be commutative rings with identity. An*A*-B-biring is an*A*-*algebra*S together with*a*lift of the*functor*HomA(S, −) from*A*-*algebras*to sets to*a**functor*from*A*-*algebras*to B-*algebras*. ...*For*any set X the ring Int(Z X ) is the*free*binomial ring*generated*by X, and*a*Z-torsion-*free*ring*A*is binomial if and only if,*for*every*a*∈*A*, there exists*a*ring homomorphism Int(Z) −→*A*sending ...##
###
Comparing free algebras in Topological and Classical Domain Theory

2010
*
Theoretical Computer Science
*

Let (Σ, E ) be

doi:10.1016/j.tcs.2010.01.021
fatcat:tirndyf2zjfxfj2zafgoaijbje
*a*parametrized equational theory*for*kTop. Then the*free**algebra**functor*F : kTop → kTop (Σ,E) preserves topological quotient maps. ... Moreover if F : kTop → kTop Σ denotes the absolutely*free**algebra**functor*, then*for*any compactly*generated*space X , the*free**algebra*(FX, {σ FX }) over X is given by (F X / ∼ E , {σ F X /∼ E }), where ... I am also very grateful to John Coleman*for*supplying me with the necessary background*on*topological*algebras*, and to Achim Jung*for*pointing me towards Christine Strüder's thesis and*for*pointing out ...##
###
FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES

1963
*
Proceedings of the National Academy of Sciences of the United States of America
*

useful

doi:10.1073/pnas.50.5.869
pmid:16591125
pmcid:PMC221940
fatcat:meyhvr7pdnax3nbrqqdwe3wxuu
*generality*can be achieved;*for*example, the constructions of*free**algebras*, tensor*algebras*, monoid rings, enveloping*algebras*of Lie*algebras*, abelianization of groups, and covariant extension ... Any*algebraic*theory*A*is equivalent to the dual of the full category of finitely*generated**free**algebras*in its associated*algebraic*category. ... where G is an object in*a*such that GU4 is*a**free**A*-*algebra**on**one**generator*. These observations enable us to completely characterize*algebraic*categories in the theorem below. ...##
###
Stable homotopy of algebraic theories

2001
*
Topology
*

*For*the theory of commutative

*algebras*we obtain

*a*ring spectrum which is related to AndreH }Quillen homology via certain spectral sequences. ...

*For*several familiar

*algebraic*theories we can identify the parameterizing ring spectrum;

*for*other theories we obtain new examples of ring spectra. ... Acknowledgements This paper is

*a*substantially modi"ed version of the main part of the author's thesis. It could not have been written without many discussions that I had with various colleagues. ...

##
###
A van Kampen spectral sequence for higher homotopy groups

1990
*
Topology
*

We define the

doi:10.1016/0040-9383(90)90022-c
fatcat:mu3frrz3bzbk7m3sz5p7bsikau
*free*Idiagram of II-*algebras**generated*by the Ki to be the*free*diagram 9{F:Ki} where each 9Ki is the*free*II-*algebra**on**generators*Ki as in 4.5. ... Naturality of this construction implies that the definition of @ in 7.1 gives*a**functor**on*the category of pairs of*free*II-*algebras*that is independent of choice of*generators*. ...*For*the*general*case let F.A and F.B be*free*simplicial resolutions of*A*and B. Let F.A 5 F.B denote the bisimplicial IIalgebra that is F,*A*0 F,J3 in dimension p, q. ...##
###
Free objects and Gröbner-Shirshov bases in operated contexts
[article]

2021
*
arXiv
*
pre-print

Various

arXiv:2103.13046v1
fatcat:f6zrznd555hwnlksmhhs3si3i4
*free*object*functors*in these operated contexts are explicitly constructed. ...*A*mild sufficient condition is found such that Φ together with*a*Gröbner-Shirshov basis of an*algebra**A*form*a*Gröbner-Shirshov basis of the*free*Φ-*algebra*over*algebra**A*in the sense of Guo et al.. ... Xing Gao, Li Guo and Yunnan Li*for*inspiring online talks and many useful comments. ...##
###
Differential (Lie) algebras from a functorial point of view

2015
*
ACM Communications in Computer Algebra
*

This relation is actually functorial, and this

doi:10.1145/2768577.2768634
fatcat:suvmgx33hjcxvpsgnykixlpqta
*functor*, as any*algebraic**functor*, is known to admit*a*left adjoint, namely the universal enveloping*algebra*of*a*Lie*algebra*. ... Other standard functorial constructions, such as the tensor and symmetric*algebras*, are studied*for**algebras*with*a*given derivation. ... This*functor*admits*a*left adjoint, known as the*free*Σ-*algebra*construction:*for**a*set X, Σ[X] then denotes the*free*Σ-*algebra**on*X (its Σ-*algebra*structure is not specified in this notation, and the ...##
###
Differential (Lie) algebras from a functorial point of view

2016
*
Advances in Applied Mathematics
*

This relation is actually functorial, and this

doi:10.1016/j.aam.2015.09.003
fatcat:bek4kpeu45cklmr2cx6kuajis4
*functor*, as any*algebraic**functor*, is known to admit*a*left adjoint, namely the universal enveloping*algebra*of*a*Lie*algebra*. ... Other standard functorial constructions, such as the tensor and symmetric*algebras*, are studied*for**algebras*with*a*given derivation. ... This*functor*admits*a*left adjoint, known as the*free*Σ-*algebra*construction:*for**a*set X, Σ[X] then denotes the*free*Σ-*algebra**on*X (its Σ-*algebra*structure is not specified in this notation, and the ...##
###
Derived functors of graded algebras

1990
*
Journal of Pure and Applied Algebra
*

*A*number of spectra1 sequences arising in homotopy theory have the derived

*functors*of

*a*graded

*algebraic*

*functor*as their E2-term. ... We also show that under these conditions the nth derived

*functor*,

*for*large n, depends only

*on*low-dimensional information. ... Acknowledgment I wish to thank my advisor, Dan Kan,

*for*his help and advice in writing this paper; also Phil Hirschhorn and Haynes Miller

*for*many useful conversations. ...

##
###
Homotopy nilpotent groups

2010
*
Algebraic and Geometric Topology
*

We prove that the set-valued

doi:10.2140/agt.2010.10.33
fatcat:rmrp4laexrgb7euaoqwflfve7q
*algebraic*theory obtained by applying π_0 is the theory of ordinary n-nilpotent groups and that the Goodwillie tower of*a*connected space is determined by*a*certain homotopy ... We prove that n-excisive*functors*of the form Ω F have values in homotopy n-nilpotent groups. ...*free*graded Lie*algebra**on**A*. ...##
###
Birings and plethories of integer-valued polynomials
[article]

2014
*
arXiv
*
pre-print

Let

arXiv:1109.3848v3
fatcat:bf67gk6kmrdjzb7bt6fyrqbyl4
*A*and B be commutative rings with identity. An*A*-B-biring is an*A*-*algebra*S together with*a*lift of the*functor*Hom_A(S,-) from*A*-*algebras*to sets to*a**functor*from*A*-*algebras*to B-*algebras*. ... This holds in particular if θ_n is an isomorphism*for*all n, which in turn holds,*for*example, if D is*a*Krull domain or more*generally**a*TV PVMD. ...*For*any set X the ring Int(Z X ) is the*free*binomial ring*generated*by X, and*a*Z-torsion-*free*ring*A*is binomial if and only if,*for*every*a*∈*A*, there exists*a*ring homomorphism Int(Z) −→*A*sending ...##
###
A Simple Construction of Derived Representation Schemes
[article]

2010
*
arXiv
*
pre-print

We present

arXiv:1010.4901v1
fatcat:7lioapqdnbbzloeejyvitqha7y
*a*simple*algebraic*construction of the (non-abelian) derived*functors*DRep_n(*A*) of the representation scheme Rep_n(*A*), parametrizing the n-dimensional representations of an associative*algebra*... We construct*a*related derived version of the representation*functor*introduced recently by M. Van den Bergh and, as an application, compute the derived tangent spaces TDRep_n(*A*) to Rep_n(*A*). ... We are also very grateful to Martin Kassabov*for*several insightful suggestions and to Frank Moore, whose computer DG*algebra*package*for*Macaulay2 we have been using extensively. ...##
###
An intrinsic definition of the Rees algebra of a module
[article]

2014
*
arXiv
*
pre-print

This paper concerns

arXiv:1402.3219v2
fatcat:nj4whu3pnvghthcl32r7e6ofl4
*a**generalization*of the Rees*algebra*of ideals due to Eisenbud, Huneke and Ulrich that works*for*any finitely*generated*module over*a*noetherian ring. ... Their definition is in terms of maps to*free*modules. We give an intrinsic definition using divided powers. ... the module into*a*certain*free*module and taking the image of the map given by applying the symmetric*algebra**functor**on*this embedding. ...##
###
PBW property for associative universal enveloping algebras over an operad
[article]

2020
*
arXiv
*
pre-print

*A*necessary condition

*on*the Hilbert series

*for*P is discovered. ... We study the notion of PBW property

*for*universal enveloping

*algebras*over an operad. In case P is Koszul

*a*criterion

*for*the PBW property is found. ... Proposition 4 . 21 . 421 The

*functors*Sh and + commute and, moreover, they map

*free*objects to

*free*objectsIn particular, the

*functors*Sh preserve the number of

*generators*of

*a*

*free*symmetric operad and ...

« Previous

*Showing results 1 — 15 out of 58,125 results*