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CATEGORIES:Junior Category Theory Seminar
SUMMARY:It's all about monoids! Algebras\, coalgebras and
Hopf algebras from a conceptual viewpoint. - Filip
Bár
DTSTART;TZID=Europe/London:20120202T140000
DTEND;TZID=Europe/London:20120202T150000
UID:TALK36227AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/36227
DESCRIPTION:The aim of this talk is to illustrate one of MacLa
ne's\nslogans in his book 'Categories for the Work
ing Mathematician'\, namely the centrality of the
concept of a monoid in mathematics.\n\nThe talk wi
ll consist of two parts. In the first part I will
explain the basic definitions beginning with inter
nal monoids and internal groups in categories with
finite products and generalize them to the framew
ork of (symmetric) monoidal categories\, i.e.\, to
internal algebras and internal Hopf algebras. In
course of the generalization we will understand th
e emergence of comonoids (coalgebras) and bimonoid
s (bialgebras). In the second part I will sketch a
hierarchy of algebraic structures with their resp
ective tensor products applying the concepts and e
lementary observations from the first part to the
category SETS. We will thereby encounter with fami
liar structures like groups\, rings and algebras (
over commutative rings) as well as less\nfamiliar
structures like monoids\, rigs\, and algebras over
commutative rigs. Finally\, I will turn to certai
n adjunctions in this hierarchy and use them to ex
plain some of the standard (and universal) example
s of Hopf algebras.
LOCATION:CMS\, MR15
CONTACT:Guilherme Lima de Carvalho e Silva
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