Geodesic
UNITARY FUNCTOR CALCULUS WITH REALITY
Glasgow mathematical journal, Tome 64 (2022) no. 1, pp. 197-230

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We construct a calculus of functors in the spirit of orthogonal calculus, which is designed to study ‘functors with reality’ such as the Real classifying space functor, . The calculus produces a Taylor tower, the n-th layer of which is classified by a spectrum with an action of . We further give model categorical considerations, producing a zigzag of Quillen equivalences between spectra with an action of and a model structure on the category of input functors which captures the homotopy theory of the n-th layer of the Taylor tower. 
TAGGART, NIALL. UNITARY FUNCTOR CALCULUS WITH REALITY. Glasgow mathematical journal, Tome 64 (2022) no. 1, pp. 197-230. doi: 10.1017/S0017089521000033
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     author = {TAGGART, NIALL},
     title = {UNITARY {FUNCTOR} {CALCULUS} {WITH} {REALITY}},
     journal = {Glasgow mathematical journal},
     pages = {197--230},
     year = {2022},
     volume = {64},
     number = {1},
     doi = {10.1017/S0017089521000033},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089521000033/}
}
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