Coming from a computer science background, I have some working knowledge on category theory but none in algebraic topology. I see many definition involves some homotopy theory which I completely have no clue, yet I see many applications of fibrations in category theory and/or related topics (e.g. a random paper: https://dlicata.wescreates.wesleyan.edu/pubs/lsr17multi/lsr17multi-ex.pdf).
My questions are: what is a (co)fibration in categorical terms? What is the intuition of (co)fibrations in categorical settings?