Double Solids, Categories and Non-Rationality

Perverse Sheaves of Categories and Non-rationality

Sextic Double Solids

We study properties of double covers of P ramified along nodal sextic surfaces such as non-rationality, Q-factoriality, potential density, and elliptic fibration structures. We also consider some relevant problems over fields of positive characteristic. 2000 Mathematics Subject Classification. Primary 14E05, 14E08, 14G05, 14G15, 14J17, 14J45. All varieties are assumed to be projective, normal, ...

Monads in double categories

Introduction The development of the formal theory of monads, begun in [23] and continued in [15], shows that much of the theory of monads [1] can be generalized from the setting of the 2-category Cat of small categories, functors and natural transformations to that of a general 2-category. The generalization, which involves defining the 2-category Mnd(K) of monads, monad maps and monad 2-cells ...

Exponentiability via Double Categories

For a small category B and a double category D, let LaxN (B,D) denote the category whose objects are vertical normal lax functors B //D and morphisms are horizontal lax transformations. It is well known that LaxN (B,Cat) ≃ Cat/B, where Cat is the double category of small categories, functors, and profunctors. In [19], we generalized this equivalence to certain double categories, in the case whe...

Jurisprudence and Rationality

  There are different concepts of rationality: specific rationality, normative rationality and instrumental rationality whose limitation covers the holistic rationality and represents the fate of rationality in the West. Thus following Hume reason became the slave of feelings and lost its authority for choosing the goal. In Islamic culture reason with its undeniable background in Shariah enjoy...