We introduce a general construction on 2-monads. develop background maps of 2-monads, their left semi-algebras, and colimits in 2-category. Then, we the colimit induced by map show that obtain structure 2-monad give characterisation its algebras. Finally, apply to 2-monads between free symmetric monoidal cartesian combine them into linear-non-linear 2-monad.

for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...

The Rational Expectations Permanent Income Hypothesis implies that consumption follows a martingale. However, most empirical tests have rejected the hypothesis. Those empirical tests are based on linear models. If the data generating process is non-linear, conventional tests may not assess some of the randomness properly. As a result, inference based on conventional tests of linear models can b...