Point: to ubnderstand fucntors study HOM. Then when such a representing object does not exist we change the definition of th words, and introduce terms like "stacks" instead of spaces so that representing objects wille exist. If more philosophers start trying to learn homotopy type theory, a bunch are bound to learn about homotopy theory, topos theory, n n-category theory, and other branches of math that have profound new things to say about concepts like equality, numbers, propositions, logical operations, space and the like where ‘new’ means post-1950s. (Basic Types) E, T Type A Type B Type (Ñ Form.) A Ñ B Type A Type (5 Form. 2.1 Types The types of MIL are summarized in Figure 2.1, below. Section 3 introduces the deductive system and certain theorems thereof. some creativity is needed to find sucha thing since strictly speaking it does not exist. tague’s original are noted, and alternative approaches to comonadic modal type theory are dis-cussed. Representing this functor means finding a uniuversal "moduli" space M with a universal family of curves over it, such that every other family of curves arises from pull back from this one. of all maps Y->X whose fibers are all curves. we can define a functor of curves over spaces, whicha ssigns to each space X, th set of all families of curves over X, i.e. When we do think of them, then we try to sklve the problem of "representability", i.e., of finding a HOM functor that is equivalent to our functor.Į.g. We just cant think of very many other functors than maps in and out of spaces. The dual functor of a vector space is the study of maps of the vector space into the scalar field.Ĭharacters are a fancy name for certain maps into a, lets see, some group of units? Does category theory subsume type theory plus#Homology is the study of maps of simplicial cells into X, plus the algebraic trick of taking formal linear combinations of them, modulo the equivalence relation imposed by taking boundaries. Does category theory subsume type theory mod#The fundamental group of X, is the study of maps of closed intervals into X, mod an equivalence relation called homotopy. A research question starts out broadly but then in the data analysis stage, the question narrows. The purpose of using GT method is to develop a theory from the data being examined. to study any object X, we look at maps of that object into other objects, or maps of other objects into it. Grounded Theory is the discovery of theory from data systematically obtained from social research. The previous example recalls that basically there is only one functor in the world, and it is called HOM.
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