A simple definition of n-category Maybe there is no simple definition of $n$-category understandable for a physicist. Then I would like to know what are the trivial $0$-category,  trivial $1$-category, trivial $2$-category, etc. How to obtain trivial $1$-category from trivial $0$-category? How to obtain trivial $2$-category from trivial $1$-category? etc 
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After that  I would like to know the definition of 0-category that allows us to obtain all the 0-categories, and the  definition of 1-category that allows us to obtain all the 1-categories etc.
I am looking for a particular kind of n-categories.
Based on the answer of André Henriques, it appears that
the trivial 0-category that I am looking for is an one-dimensional vector space. A less trivial 0-category is a n-dimensional vector space, which is a composition of n trivial 0-categories. The trivial 1-category is a category of vector spaces, with only one simple object, which is a trivial object corresponding to an one-dimensional vector space, and the composition of several simple objects gives us a composite object which corresponds to a finite dimensional vector space.
I also guess that the trivial 0-category (ie an one-dimensional vector space) and the composite 0-categories (ie n-dimensional vector spaces) are all the 0-categories (of this type). The category of all vectors spaces is the "trivial" 1-category. All possible 1-categories (of this type) are fusion categories. Along this line, the "trivial" 2-category is the collection of all fusion categories. Then what are the most general 2-categories. 
We need a definition here. 
The purpose of this question is not to find out an answer, but to find out a proper way to ask the question. I hope after some exchanges, I know what really is the question that I want to ask. 
 A: I'll interpret "definition understandable for a physicist" to mean "please give me a bunch of examples to keep in mind". Here you go:
Here are some examples of 0-categories:


*

*a set with $n$ elements.

*a vector space of dimension $n$ (strictly speaking, that's an example of a 0-category with extra structure, namely a linear structure)
Here are some examples of 1-categories:


*

*the category of all sets.

*the category of all groups.

*the category of all Lie algebras.

*the category of all vectors spaces (once again, that's an example of a category with extra structure, namely a linear structure)

*the category Mod-$A$ of all modules over a fixed algebra $A$ (once again, this has a linear structure).

*the category of d-dimensional cobordisms between (d-1)-dimensional manifolds.

*the fundamental groupoid of a topological space.
Here are some examples of 2-categories:


*

*the 2-category of algebras, bimodules, and maps between bimodules.

*the 2-category of cobordisms, where you allow corners of codimension 2.

*the fundamental 2-groupoid of a space (you look at points of the space, paths between points, and homotopies between paths).

*the 2-category of categories, functors, and natural transformations.

*the 2-category of $\mathcal C$-modules, where $\mathcal C$ is a fixed tensor category (again, there are notions of functors, and of natural transformations between those)

*the 2-category of CFTs, their topological defects, and all possible (topological) field insertions.
Here are some examples of n-categories that work for any $n$:


*

*the n-category of cobordisms, where you allow corners up to codimension $n$.

*the fundamental n-groupoid of a topological space.

*the category of $\mathcal C$-modules, where $\mathcal C=(\mathcal C,\otimes)$ is an $(n-1)$-category equipped with a monoidal product.

*the collection of all $(n-1)$-categories.

*the collections of all QFTs of dimension $n$, along with their (topological) defects of all possible dimensions (i.e. starting from domain walls, and going all the way down to point-like fields).
