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SUMMARY:Chiara Sava (Charles University\, Prague)
DTSTART:20250930T150000Z
DTEND:20250930T163000Z
DTSTAMP:20260422T174244Z
UID:tandg/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/tandg/33/">D
 ifferential graded algebras in differential categories</a>\nby Chiara Sava
  (Charles University\, Prague) as part of Topology and Geometry Seminar (T
 exas\, Kansas)\n\n\nAbstract\nDifferential categories\, introduced in last
  week's talk by Jean-Simon Pacaud Lemay\, provide a categorical framework 
 for the algebraic foundations of differential calculus. Within this settin
 g we can capture familiar notions such as derivations\, Kähler differenti
 als\, differential algebras and de Rham cohomology. Along this line\, in t
 his talk\, we will show how to define differential graded algebras in a di
 fferential category. In the case of polynomial differentiation\, this cons
 truction recovers the classical commutative differential graded algebras\,
  while for smooth functions it yields differential graded $C^\\infty$-ring
 s in the sense of Dmitri Pavlov. To further justify our definition\, we wi
 ll explain how the monad of a differential category can be lifted to its c
 ategory of chain complexes and how the algebras of the lifted monad corres
 pond precisely to differential graded algebras of the base category\, with
  the free ones given by the de Rham complexes. Finally\, we will discuss h
 ow the category of chain complexes of a differential category is itself a 
 differential category\, pointing towards the prospect of differential dg-c
 ategories. This is joint work with Jean-Simon Pacaud Lemay.\n
LOCATION:https://researchseminars.org/talk/tandg/33/
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