144 citations · 687 across the 51 of their papers we have counts for
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N-spherical functors and categorification of Euler's continuants
Tobias Dyckerhoff, Mikhail Kapranov, Vadim Schechtman
Euler's continuants are universal polynomials expressing the numerator and denominator of a finite continued fraction whose entries are independent variables. We introduce their ca…
PROBs and perverse sheaves II. Ran spaces and 0-cycles with coefficients
Mikhail Kapranov, Vadim Schechtman
We consider the space Z(C,L) of 0-cycles on the complex line C with coefficients in a commutative monoid L subject to certain conditions. Such spaces include the symmetric products…
PROBs and perverse sheaves I. Symmetric products
Mikhail Kapranov, Vadim Schechtman
Algebraic structures involving both multiplications and comultiplications (such as, e.g., bialgebras or Hopf algebras) can be encoded using PROPs (categories with PROducts and Perm…
Symmetric and exterior powers of categories
Nora Ganter, Mikhail Kapranov
We define symmetric and exterior powers of categories, fitting into categorified Koszul complexes. We discuss examples and calculate the effect of these power operations on the cat…