I am trying to understand the depth of an output of a convolutional layer. For example, the first convolutional layer has the shape 3x3x32. So there are 32 filters with shape 3x3, but each filter has 3 layers and these 3 layers convolve over 3 layers of the input. At the end, values of the 3 layers are summed up and to generate 1 layer. For 32 filters, we get an output with 32 layers.
If we look at the next layer, 64 filters with size 3x3 and each filter should have 32 layers. Because input has 32 layers. Is this inference true? If it is not, how does it work?