Using custom post template

$cat->1176 cannot be a property of an object.

PHP Manual:

A valid variable name starts with a letter or underscore, followed by any number of letters, numbers, or underscores. As a regular expression, it would be expressed thus: ‘[a-zA-Z_\x7f-\xff][a-zA-Z0-9_\x7f-\xff]*’

Use $cat->term_id and compare it’s value with the number you’re out for.

And … don’t use anonymous functions. They cannot be cached by opcode caches like APC and they are hard to debug – as you have seen. Plus, if someone wants to remove this filter in a child theme, that’s now very, very hard.