We investigate how people generalize from observing one (Experiment 1) or several (Experiment 2) causal interactions between pairs of objects. In each case, participants see an agent object act on a recipient object, causing some changes to the recipient. In line with human capacity for few-shot concept learning, we find systematic patterns of causal generalizations favoring simpler causal laws that extend over categories of similar objects. Our experiments provide clues about both the cognitive processing, and causality-specific inductive biases involved in causal generalization. In Experiment 1, we find a clear generalization-order effect in which individuals' final beliefs are crystallised by their initial generalizations. In both experiments, we find a causal asymmetry in the formation of causal categories, in which participants preferentially identify causal laws with features of the agent objects rather than recipients. To explain this, we develop a computational modeling framework that combines program induction (about the hidden causal laws) with non-parametric category inference (about their domains of influence). We demonstrate that our modeling approach can both explain the order effect and capture the causal asymmetry, and in doing so, outperforms a naive Bayesian account while providing a computationally plausible mechanism for real world causal generalization.