category

• a [[thing]].
  • [[pull]] [[categories]] [[category theory]]
  • [[collection]] of [[objects]] and [[morphisms]].
  • [[wp]] https://en.wikipedia.org/wiki/Category_(mathematics) pull
    • [[go]] [[wp]]

category

tags : [[category theory]]

source : [[ACT4E - Session 1 - Transmutation]]

A category is specified by four characteristics:

1. Objects, \(X\)
2. Morphisms, \(X \to Y\). For every pair of objects in a category there exists a set whose elements map X to Y (this set could be called \(Hom(X,Y)\))
3. Identitiy morphisms, a morphism \(X \to X\)
4. Composition. Given morphisms f and g, there exists a morphism h such that \(h = f \circ g\)

Additionally, categories adhere to the following conditions:

1. Unitality: for any morphism in the category \(X \to Y\), \(id_x \circ f = f = f \circ id_y#\)
2. Associativity: given morphisms f, g, and h in the category, \((f \circ g) \circ h = f \circ (g \circ h)\)

• [[flancian]] https://social.coop/@flancian/108584858543201574 pull
• [[yog]] https://mathstodon.xyz/@yog/109255204950545835 pull
• [[yog]] https://mathstodon.xyz/@yog/109255193158307281 pull

• [[flancian]] https://twitter.com/flancian/status/1543664723257966592 pull