# Bayesian analysis: what is the kernel of Cauchy distribution

Here is the Cauchy model by putting 𝑛 = 1, 𝜇 = 𝜃, 𝜎 = 1 in the student's t-model:

$$f(y|\theta)=\frac{1}{\pi\cdot(1 + (y - \theta)^2)}$$

Is the kernel (the parts that contain y) $$\frac{1}{(1 + (y - \theta)^2)}$$? Or there is a way to further extract parts that have nothing to do with y? Thank you in advance!