Basilar-Artery
发表于 2025-3-25 05:12:13
Special Limits,This chapter covers two useful types of limits (and colimits): The filtered limits, which are limits taken over preordered sets which are directed (and, more generally, over certain filtered categories), and the “ends”, which are limits obtained from certain bifunctors, and which behave like integrals.
声明
发表于 2025-3-25 10:49:44
Structures in Categories,In this chapter, we will examine several conceptual developments. We start with the idea of an “internal” category, described by diagrams within an ambient category. We then go on to study the sequences of composable arrows in a category — they constitute the “nerve” of the category, which turns out to be a simplicial set.
ELUDE
发表于 2025-3-25 14:18:45
Introduction, of arrows. Each arrow . : . → . represents a function; that is, a set ., a set ., and a rule . ↦ . which assigns to each element . ∈ . an element . ∈ .; whenever possible we write . and not .(.), omitting unnecessary parentheses.
狗舍
发表于 2025-3-25 19:42:08
Constructions on Categories,n a set-theoretical basis in the next section. Hence for this section a category will not be described by sets (of objects and of arrows) and functions (domain, codomain, composition) but by axioms as in § I.1.
负担
发表于 2025-3-25 20:19:33
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横截,横断
发表于 2025-3-26 02:45:40
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Facet-Joints
发表于 2025-3-26 08:00:14
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cluster
发表于 2025-3-26 11:50:31
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诱导
发表于 2025-3-26 13:43:12
Karin Bruckmüller,Ulrich Schrothn a set-theoretical basis in the next section. Hence for this section a category will not be described by sets (of objects and of arrows) and functions (domain, codomain, composition) but by axioms as in § I.1.
妨碍议事
发表于 2025-3-26 17:06:11
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