A primer on triangle functions I

Summary.

This primer aims at providing an overview of existing concepts and facts about triangle functions as they have been presented in [41]. Moreover, it contains new results on triangle functions and proofs for results not easily available. In this first part we present the most important classes of triangle functions, based on the recent notions of semicopula, quasicopula, as well as the more traditional ones of t-norm, copula and (generalized) convolution. We close this part by listing some basic results needed for the applications (inequalities, aspects of stability and invariance of subspaces) and outlining a few open questions.