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SUMMARY:Cartesian differential categories as skew enriched categories - Ri
 chard Garner (Macquarie University)
DTSTART:20210608T090000Z
DTEND:20210608T103000Z
UID:TALK160930@talks.cam.ac.uk
CONTACT:José Siqueira
DESCRIPTION:Cartesian differential categories are an abstraction of the\nc
 ategory of smooth maps between Euclidean spaces. Their main feature is an 
 operator assigning to each map f:A -> B another map Df: A*A --> B called t
 he differential of f\, subject to a list of axioms.\n\nIn this talk\, we e
 xplain the slightly surprising fact that cartesian differential categories
  are actually a kind of enriched category. The enrichment base is the cate
 gory of k-vector spaces\, but the monoidal structure is not the usual one\
 , but rather a skew-monoidal warping of it with respect to a monoidal como
 nad. The comonad at issue is not ad hoc\, but in fact the initial one imbu
 ing k-vector spaces with the structure of a model of intuitionistic differ
 ential linear logic.\n\nThis is a report on joint work with JS Lemay.\n\nZ
 oom link: \n https://maths-cam-ac-uk.zoom.us/j/92631058994?pwd=TlNIMnoxRXJ
 4YkVpa2VFdUtvbldDZz09
LOCATION:Zoom (Meeting ID 926 3105 8994\, passcode  345661)
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