Non-exact integral functors

How Large Are Left Exact Functors?

For a broad collection of categories K, including all presheaf categories, the following statement is proved to be consistent: every left exact (i.e. finite-limits preserving) functor from K to Set is small, that is, a small colimit of representables. In contrast, for the (presheaf) category K = Alg(1, 1) of unary algebras we construct a functor from Alg(1, 1) to Set which preserves finite prod...

On Stable Equivalences Induced by Exact Functors

Let A and B be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence α between A and B such that α is induced by exact functors. We present a nice correspondence between indecomposable modules over A and B. As a consequence, we have the following: (1) If A is a self-injective algebra, then so is B; (2) If A and B are finite dimensional algebras over an algeb...

Non-additive Functors, Their Derived Functors, and the Suspension Homomorphism.

3E. L. Post, J. Symb. Logic, 12, 1-11, 1947. 4In the sense of Post, the word problem for Z is reducible to that for sp (2:). 5 W. Magnus, Math. Annalen, 106, 295-307, 1932. 6 DanaScott, abstract, J. Symb. Logic, 21, 111-112, 1956. 7Marshall Hall, J. Symb. Logic, 14, 115-118, 1949. 8 G. Higman, B. H. Neumann, and H. Neumann, J. London Math. Soc., 24, 247-254, 1949. 9 As defined, UG, Part I, p. 2...

Exact solutions of nonlinear interval Volterra integral equations

Exact Path Integral for 3D Quantum Gravity.

Three-dimensional Euclidean pure gravity with a negative cosmological constant can be formulated in terms of the Chern-Simons theory, classically. This theory can be written in a supersymmetric way by introducing auxiliary gauginos and scalars. We calculate the exact partition function of this Chern-Simons theory by using the localization technique. Thus, we obtain the quantum gravity partition...