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CATEGORIES:Category Theory Seminar
SUMMARY:Infinitesimal models of theories - Filip Bár (DPMM
S)
DTSTART;TZID=Europe/London:20161018T141500
DTEND;TZID=Europe/London:20161018T151500
UID:TALK68626AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68626
DESCRIPTION:Can we make precise the idea that the geometry of
a space is affine\, euclidean\, or projective at a
n infinitesimal level?\n\nYes\, we can\, in princi
ple. In fact\, there is a construction for first-o
rder theories\, which we call their infinitesimali
sation. The models of the infinitesimalisation may
be considered as spaces\, which are models of tha
t theory at an infinitesimal level.\n\nWhat is con
sidered to be at an infinitesmal level for a space
is defined by a structure\, which we call infinit
esimal structure. For a one-sorted first-order the
ory the construction of infinitesimalisation intro
duces an infinitesimal structure\, replaces every
operation by a partial operation with the domains
of definition specified by the infinitesimal struc
ture\, and every relation is required to factor th
rough the infinitesimal structure. The axioms of t
he theory are adapted accordingly.\n\nWith these n
otions at hand we can show that every formal manif
old in Synthetic Differential Geometry is an infin
itesimal model of the algebraic theory of affine c
ombinations\, and that for every Lie group the spa
ce of points\, which are infinitesimal neighbours
of the neutral element\, yields an infinitesimal m
odel of a group.
LOCATION:MR5\, Centre for Mathematical Sciences
CONTACT:Tamara von Glehn
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