for loop concatenating files that share part of their common basename (paired end sequencing reads)

Question

I'm trying to concatenate a bunch of paired files into one file (for those who work with sequencing data, you'll be familiar with the paired-end read format).

For example, I have

SLG1.R1.fastq.gz
SLG1.R2.fastq.gz
SLG2.R1.fastq.gz
SLG2.R2.fastq.gz
SLG3.R1.fastq.gz
SLG3.R2.fastq.gz

etc.

I need to concatenate the two SLG1 files, the two SLG2 files, and the two SLG3 files.

So far I have this:

cd /workidr/slg/diet_manip/filtered_concatenated_reads/nonhost
for i in *1.fastq.gz
  do
  base=(basename $i "1.fastq.gz")
  cat ${base}1.fastq.gz ${base}2.fastq.gz > /workdir/slg/diet_manip/filtered_concatenated_reads/cat/${base}.fastq.gz
  done

The original files are all in the /filtered_concatenated_reads/nonhost directory, and I want the concatenated versions to be in /filtered_concatenated_reads/cat

The above code gives this error:

-bash: /workdir/slg/diet_manip/filtered_concatenated_reads/cat/basename.fastq.gz: No such file or directory

Any ideas?

Thank you!!