Let's assume that we are talking about 2D convolutions applied on images.
In a grayscale image, the data is a matrix of dimensions $w \times h$, where $w$ is the width of the image and $h$ is its height. In a color image, we normally have 3 channels: red, green and blue; this way, a color image can be represented as a matrix of dimensions $w \times h \times c$, where $c$ is the number of channels, that is, 3.
A convolution layer receives the image ($w \times h \times c$) as input, and generates as output an activation map of dimensions $w' \times h' \times c'$. The number of input channels in the convolution is $c$, while the number of output channels is $c'$.
My confusion is that will CNN operate on the fused representation of the data if $c =2$ or 3 or 4 etc? Or does it operate on each channel at a time and then stacks the results? Say I have 4 channels each channel is a 2D matrix then would CNN internally form a fusion of the 4 channels and make some sort of a representation?