Is there an easy way of remembering the direction of arrows between morphisms in Categories? 


The direction of arrows so confuses me: products and co-products, (**EDIT-** Also, pull-backs, pushouts, contra/co-variant functors) and their universal mapping properties. I have to look back into Lang's Algebra and revise it every time. 


Please tell if the question is not appropriate.



Remembering arrows' directions in basic Category Theory
I think that the best way to remember these things is to have a good example of each of these constructions in your head. If you remember the direction of the arrows for them, and if the example is "natural" enough the direction will be obvious, you will have the direction in the general case. Just watch out, sometimes two constructions will yield the same things in specific examples so you want to have examples that distinguish between the various notions. An example of this is that finite products and finite co-products have a habit of being the same in categories in which I search for examples (additive categories like categories of representations).


