2 category expression pdf 2025

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The document is a guide for completing the Expression of Interest (EOI) form for the Investor (Investor 2 Category) visa in New Zealand. It outlines the process for potential migrants to express their interest in migrating as investors, detailing necessary forms, eligibility criteria, and required documentation. The guide emphasizes the importance of providing accurate information and includes sections on personal details, family information, investment funds, and health requirements. It also highlights the points-based system used to assess applicants and the conditions that must be met if residency is granted.

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What is a 2 category?

Category of small categories The archetypal 2-category is the category of small categories, with natural transformations serving as 2-morphisms; typically 2-morphisms are given by Greek letters (such as. above) for this reason. The objects (0-cells) are all small categories, and for all objects A and B the category.

What is a monad in category theory?

In category theory, a branch of mathematics, a monad is a triple consisting of a functor T from a category to itself and two natural transformations that satisfy the conditions like associativity. For example, if are functors adjoint to each other, then together with. determined by the adjoint relation is a monad.

What is a Monad in a 2-category?

If C is a 2-category, a monad on an object CC consists of an endomorphism T:CC and a pair of 2-morphisms, :idCT and :T∘TT with some coherence conditions.

What is an example of a 2-category?

The basic example of a 2-category is CAT itself, with natural transformations as 2-cells (squares). As category theory describes set-like constructions, 2-category theory describes category-like constructions. You can usually build up categories with as objects sets with extra structure.

What is equivalence in a 2-category?

A morphism f : A B in a 2-category K is said to be an equivalence if there exist a morphism g : B A and isomorphisms gf = 1A and fg = 1B.

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What are two categories?

The easiest definition of 2-category is that it is a category enriched over the cartesian monoidal category Cat. Thus it has a collection of objects, and for each pair of objects a category hom ( x , y ) .

What is a monad in simple terms?

What is a Monad? A monad is an algebraic structure in category theory, and in Haskell it is used to describe computations as sequences of steps, and to handle side effects such as state and IO. Monads are abstract, and they have many useful concrete instances. Monads provide a way to structure a program.

2 category expression pdf 2025

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