In order to manage the issue of diversity of regulatory vision, States may, to some extent, harmonize substantive regulation—eliminating diversity. This is less likely than States determining unilaterally or multilaterally to develop manageable rules of jurisdiction, so that their regulation applies only in limited circumstances. The fullest realization of this “choice of law” solution would involve geoblocking or other technology that divides up regulatory authority according to a specified, and a perhaps agreed, principle. Geoblocking may be costly and ultimately porous, but it would allow different communities to effectuate their different visions of the good in the platform context. To the extent that the principles of jurisdiction are agreed, and are structured to be exclusive, platforms would have the certainty of knowing the requirements under which they must operate in each market. Of course, different communities may remain territorial states, but given the a-territorial nature of the internet, it may be possible for other divisions of authority and responsibility to develop. Cultural affinity, or political perspective, may be more compelling as an organizational principle to some than territorial co-location.

The theme of this chapter is the relation between the initial algebra for a set functor and the terminal coalgebra, assuming that both exist and that the endofunctor is non-trivial. We introduced a notion called pre-continuity. Pre-continuous set functors generalize finitary and continuous set functors. For such functors, the initial algebra and the terminal coalgebra have the same Cauchy completion and the same ideal completion: the $\omega$-iteration of the terminal-coalgebra chain. It follows that for a non-trivial continuous set functor, the terminal coalgebra is the Cauchy completion of the initial algebra.

On October 27, 2022, the Digital Services Act (DSA) was published in the Official Journal of the European Union (EU). The DSA, which has been portrayed as the Europe’s new “Digital Constitution”, sets out a cross-sector regulatory framework for online services and regulates the responsibility of online intermediaries for illegal content. Against this background, this chapters provides a brief overview of recent regulatory developments regarding platform responsibility in the EU. The chapter seeks to add a European perspective to the global debate about platform regulation. Section 3.1 provides an overview of the regulatory framework in the EU and recent legislative developments. Section 3.2 analyses different approaches regarding the enforcement of rules on platform responsibility. Section 3.3 takes a closer look at the regulation of content moderation by digital platforms in the EU. Finally, Section 3.4 adds some observations on the international effects of EU rules on platform responsibility.

While the social media and digital platforms started with an objective to enhance social connectivity and information sharing, they also present a significant challenge in content moderation resulting in spreading disinformation. Disinformation Paradox is a phenomenon where an attempt to regulate harmful content online can inadvertently amplifies it. The social media platforms often serve as breeding grounds for disinformation. This chapter discusses the inherent difficulties in moderating content at a large scale, different responses of these platforms and potential solutions.

This chapter examines China’s approach to platform responsibility for content moderation. It notes that China’s approach is rooted in its overarching goal of public opinion management, which requires platforms to proactively monitor, moderate, and sometimes censor content, especially politically sensitive content. Despite its patchy and iterative approach, China’s platform regulation is consistent and marked by its distinct characteristics, embodied in its defining of illegal and harmful content, its heavy platform obligations, and its strong reliance on administrative enforcement measures. China’s approach reflects its authoritarian nature and the asymmetrical power relations between the government and private platforms. This chapter also provides a nuanced understanding of China’s approach to platform responsibility, including Chinese platforms’ "conditional liability" for tort damages and the regulators’ growing emphasis on user protection and personal information privacy. This chapter includes a case study on TikTok that shows the interplay between the Chinese approach, oversees laws and regulations and the Chinese online platform’s content moderation practices.

The rational fixed point of an endofunctor is a fixed point which is in general different from its initial algebra and its terminal coalgebra. It collects precisely the behaviours of all ‘finite’ coalgebras of a given endofunctor. For sets, they are those with finitely many states. Examples of rational fixed points include regular languages, eventually periodic and rational streams, etc. To study the rational fixed point in categories beyond sets, we discuss locally finitely presentable categories, and we do so in some detail. We characterize the rational fixed point as an initial iterative algebra. The chapter goes into details on many examples, such as rational fixed points in nominal sets. It discusses the rational fixed point and several other fixed points as well, and it summarizes much of what is known about them.

Chapter 6 may be regarded as an extension of Chapter 5, aiming to discuss several important aspects concerning secondary or psychological drives, given that digital services widely consumed by the general population tend to cater to the satiation of one or more of these drives. These drives or needs have emerged within a cultured society that reaches into the human psyche, taking on a significant role in regulating interactions among different members of society. With the advent of social networks, and the continuous interactions we engage in through them, certain psychological drives such as status or control over identity are becoming a powerful mobilizing force for goal-directed behavior. Hence, it has been deemed timely to delve deeper into some specific drives in this regard.

This chapter provides examples of the central concepts of the book: initial algebras and terminal coalgebras. These are mainly for polynomial endofunctors on the category of sets, but also for such functors on sorted sets, nominal sets, and presheaves. We discuss connections to induction and recursion and to their duals, coinduction and corecursion, and also to bisimulation. We present Lambek’s Lemma, a result used throughout the book.

There is a growing concern about the evolution of violent extremism in the digital era. This chapter presents historical progression and current state of how extremists have used digital advancements to increase their reach and influence for their own nefarious purposes. This chapter also discusses the challenges due to encryption and the need for a strategic collaboration and comprehensive whole-of-society approach to combat the threats effectively.

This chapter presents simple and reachable coalgebras and constructions of the simple quotient of a coalgebra and the reachable part of a pointed one. It introduces well-pointed coalgebras: those which are both reachable and simple. Well-pointed coalgebras constitute a coalgebraic formulation of minimality of state-based systems. For set functors preserving intersections, we prove that the terminal coalgebra is formed by all well-pointed coalgebras, and the initial algebra by all well-founded, well-pointed coalgebras (both considered up to isomorphism) with canonical structures.

The current chapter addresses one of the most controversial concepts in psychology due to the challenge it poses to study from a methodological perspective: the mind. The chapter’s objective is to inform the reader that when accessing digital services, users come with preformed expectations shaped into mental or neural representations, a result of their previous experiences with the service or from what they have learned through social interactions with others. In the decision-making process, where users determine whether to use a digital service or others, they base their choice on a cognitive unit comprised of different mental representations that link a behavior to a reward. The behavior that is decided upon (which would include the use of the digital service) generates a set of expectations, which will be compared to the actual experience. The outcome of this expectation-reality comparison will elicit an emotional response that will become associated with the digital service, altering its value for the user. The congruence between expectation and reality is a fundamental requirement for a cognitively ergonomic design of digital services. Therefore, digital behavior designers must ensure that user expectations align with the reality of interacting with the digital tool. Designing user expectations should be one of the focal points in the design of digital behaviors, as a mismatch between expectation and reality can produce aversive emotions that may lead to the abandonment of the service.

Platform governance and regulation have been salient political issues in Brazil for years, particularly as part of Congress’ response to democratic threats posed by former President Bolsonaro. The question became even more important after the January 8th attempted insurrection in Brasília, which many blame on social media. This includes the newly installed Lula administration. In a letter read on the February 2023 UNESCO “Internet for Trust” global conference, the President, now in his third (non-consecutive) term in office wrote that the attack on the nation’s seats of power was “the culmination of a campaign, initiated much before, and that used, as ammunition, lies and disinformation,” which “was nurtured, organized, and disseminated through several digital platforms and messaging apps.” The new administration has made platform regulation a policy priority, with regulatory and administrative pushes across the board. Brazil has been a battleground where proposals for platform responsibility have been advanced — and disputed.

This chapter takes the iterative construction of initial algebras into the transfinite, generalizing work in Chapters 2 and 4. It begins with a brief presentation of ordinals, cardinals, regular cardinals, and Zermelo’s Theorem: Monotone functions on chain-complete posets have least fixed points obtainable by iteration. When a category has colimits of chains, if an endofunctor preserves colimits of chains of some ordinal length, then the initial-algebra chain converges in the same number of steps. We discuss the precise length of that iterative construction. We introduce the concept of smooth monomorphisms, providing a relation between iteration inside a subobject poset and in the ambient category. We prove the Initial Algebra Theorem: Under natural assumptions related to smoothness, the existence of a pre-fixed point of an endofunctor guarantees the existence of an initial algebra.