# Output dimension of convolutional layer - where did color dimension go?

I'm working with a Convolutional Neural Network in Matlab, and I'm struggling to understand the output dimensionality of a convolutional layer.

The input is an image: 227 x 227 x 3 (last dimension is rgb). Filter size is 11 x 11, and there are 96 filters. Vertical and horizontal stride is 4. There is no padding.

I tried calculating the output dimensionality as follows:

output_width = (Width - FilterWidth + 2*Padding)/StrideHorizontal = (227 - 11 + 0)/4 = 55.

Now, I expected an output of 55 x 55 x 3 x 96, as there are 96 filters, but I get 55 x 55 x 96. What I don't understand is, what happened to the color dimension?

The filter dimension replaces the channels in the convolutional layer: $$3$$ becomes $$96$$ it isn't lost.
Each one of the pixels 96 in a specific location are computed as the weighted average of the $$11\times11\times3$$ pixels in the same region of the image.